Following Aisha's falling behind the caravan, the hypocrites and some other individuals who were also perhaps some of the proponents and supporters of the first caliph spread gossips and slanderous lies accusing Aisha of having an affair with another man. This event was later known as the event of Ifk (slander). God revealed some verses to reject this gossip. The Shiites, who had no role in spreading this rumor, do not accept such an accusation but they do have some other criticisms about Aisha, criticisms that have nothing to do with the "slander" story. Their criticisms and objections relate to Aisha's misdemeanors towards the Prophet (s) and annoying of him. There is a verse in this regard in Sura al-Ahzab of the Quran which explicitly deals with this issue and Sunni exegetes and historians have also made mention of this point in their works. Also, her interference in the murder of the third caliph and thereupon launching a bloody battle against the Commander of the Faithful, Ali (a.s) are some of the instances which have given rise to some questions in the minds of many Muslims including those who lived in her time period. Unfortunately, so far no appropriate answer has been given to such questions.
In order to give a clear answer to the question, we must deal with various subjects so that after analyzing them, we may reach an appropriate conclusion in this regard. Those subjects are the following:
1. Which is the verse in the Quran that you intend to refer to and what story does it relate to?
2. What does the term "momeen" (faithful) mean in the verse of the Quran? Do you mean to say that if a person is described as momeen in the Quran, he turns into a legendary and unobjectionable personality?!
3. To what extent can men influence the lives of their wives? If a woman is a prophet's wife, does it mean that she is immune to all kinds of errors and mistakes?
4. What is Shi'ah belief about Aisha? What are our criticisms of Aisha?
We will discuss the above questions in the same order:
1. Most probably, the intended verse in your question is verse 23 of Sura al-Al-Noor which was revealed in connection with the "slander" story. It says:
"ان الذین یرمون المحصنات الغافلات المؤمنات لعنوا فی الدنیا و الآخرة و لهم عذاب عظیم"
"Surely those who accuse chaste believing women, unaware (of the evil), are cursed in this world and the hereafter, and they shall have a grievous chastisement."
Some commentators of the Holy Quran is of the view that this verse is general and that it applies to every person who accuses a chaste woman of an indecent action. Such an interpretation seems to be more coherent and suitable as it can be inferred from the context of the verse. Some other scholars are of the view that the verse is particular to wives of the Prophet (s). There is also a third group of scholars who say that the said verse relates to the "slander" story and the person of Aisha. If so, all these interpretations lead to a fixed conclusion which is the meanness and abominableness of accusing others without a valid reason because it is not wise to say that it is mean to accuse only the wives of the Prophet not those of others. Therefore, assuming that your interpretation of the verse is correct and that it relates to the "slander" story and Aisha, then we have to see what the "slander" [Ifk] story is.
It is better to hear the story from Aisha herself since she has narrated this event at length but the summary of the story narrated by her as under:
“Whenever the Prophet (S) would intend to go on a journey, he would cast lots amongst his wives. So whoever’s lot would be picked, would accompany the Prophet (S). So he cast these lots on one of these expeditions and my name came up, so I traveled with the Prophet (S). This was after the verses pertaining to hijab were revealed and therefore I would travel in my hawdaj and be carried in it. After the expedition had finished and we were returning to Madinah, the Prophet (s) gave orders to camp the night outside of Madinah. When the orders were given to encamp, I stood up and walked away from the army to relieve myself. When I returned, I felt my chest and noticed that my onyx necklace had broken [and fallen] so I returned to where I had been [to search for it]. I was delayed in searching for it and in the meantime the people that were assigned to carry my hawdaj had already placed it on top of the camel, presuming that I was [back] in it. So they sent the camel forward and I found my necklace after they had gone. By the time I returned to the caravan camping ground, there was not a soul in sight. One of the companions was also lagging behind the army. For some reason he was late so he was not up with the army and he walked up to my place. We both moved out together and reached the army of the Messenger of Allah. This led some people to spread gossip about me and finally the verse of Ifk was revealed and which was a proof of my chastity. 
Now, we should see as to who were most involved in spreading this gossip. What is understood from the historical narrations in this regard is that Abdullah bin Ubai, Hassan bin Thabit and Musattah bin Athatha were at the top gossipers. As for the social position of those who spread the gossip, this is an inquiry that also needs to be replied. The answer to this inquiry helps us reach a correct analysis of the story:
A) Abdullah bin Ubai: He is one of the famous and renowned hypocrites who left no stone unturned to weaken the Holy Prophet (s)? It is very natural on his part to exploit this incident for his own benefit.
B) Hassan bin Thabit: He is a poet who has composed a lot of poems on different occasions about different events during the period of the Holy Prophet (s) but Shiites criticize him for his performance in the ensuing years after the demise of the Prophet (s). His actions against the Commander of the Faithful are not approved of by Shiites. Hassan is one of the poets who composed different poems about the first caliphs and even in praise of Aisha but he also had a hand in this gossip. Years later, after the demise of the Holy Prophet (s) Hassan composed a poem in which he expressed his willingness to meet Aisha but she rebuked him expressly for his involvement in the accusation or what was known as "slander event". 
C) Musattah bin Athatha: This man was Abu Bakr's maternal cousin who due to poverty was also finally supported by him. Sunni exegetes are of the view that Abu Bakr no longer supported him after the slander incident when he learned that he was involved in accusing his daughter. But then a verse was revealed saying that it was not good to do such an action and Abu Bakr started giving him his support afresh.
Almost all Shi'ah jurisprudents have narrated the story in the same way as reported in Sunni books and they believe that the verse of Ifk (slander) is in regard with the same event. There is a small minority of commentators of the Quran who do not consider this verse to be about Aisha saying that the verse has been about Mariyah Qibtiyah. This was a brief explanation of the story of "Ifk" about which the verse in question has been revealed.
2. The next point to mention is that even if we suppose that the verse in question makes an explicit reference to Aisha's iman (faith) then our question is: Does the verse imply that whosoever is described in the Quran as faithful, it is guaranteed that he/she will remain faithful until the end of his/her life or that his/her actions will not be subject to any criticism?! We do not accept such an interpretation because, as the Quran says, there were some believers who returned to disbelief and infidelity and became even further stern than other disbelievers. Also, the Holy Quran has many a time addressed some people as momeen (faithful) yet it has threatened and rebuked them in the severest manner. Some Sunni brothers have made the same mistake about the companions of the Holy Prophet (s). Relying on some Quranic verses which implies God's pleasure and satisfaction with the companions at a particular period of time, the Sunni scholars have considered their positions higher than they can be objected and they believe that despite the fact that many of the companions fought one another and engaged in bloodshed, it is not permissible for other Muslims to criticize them or make any remarks about them. Thus they believe that every companion of the Prophet (s) irrespective of whether he is a murderer or the murdered or impartial in an event must be respected. You can read more by referring to questions 3499 and 3517 on our website.
The conclusion we draw is that even if we assume that your interpretation of the verse is correct and that the term "faithful" in it concerns Aisha, we cannot, with reference to the said verse, consider Aisha to be a personality beyond any criticism.
3. Perhaps, some may think that Aisha's spousal relationship to the Holy Prophet (s) is a reason that makes us avoid raising any criticisms about her. We must say in this regard that if we go through the religious texts and Quran on top of them, we will find out that women have an independent personality and that it is they themselves who decide to be good or bad at the end of the day. Nevertheless, if we want to assess women in relation to their husbands, we can divide them into five separate groups:
1-3. The First group consists of women who both themselves and their husbands believe firmly in God and follow His commandments. Naturally, such an understanding is the best possible situation and believing men always pray to God to grant them such a success and bestow upon them such prosperity. They say: "Our Lord! Grant unto us wives and offspring who will be the comfort of our eyes, and give us (the grace) to lead the righteous." Couples like the Prophet (s) and the Mother of the Faithful, Khadijah and also the Commander of the Faithful, Ali (a.s) and the greatest lady of the worlds, Fatima (s.a) can be introduced as the most manifest examples of this group.
2-3. The second group consists of wicked and cruel women who, with the help and collaboration of their irreligious husbands, endeavor to oppose the prophets and divine saints. Unlike the first group, such couples will be in the worst abode.
The Holy Quran has given an example of such women in Sura al-Masad. It reproaches Abu Lahab who despite having family relationship with the Prophet (s) hurt and tormented him. Also, his wife Umm Jamil, sister of the great enemy of Islam, Abu Sufyan has been reproached. 
3-3. There are also women who fail to get married in their lives due to the unavailability of means or opportunity but such women remain chaste and religiously adherent and Allah bestows special attention to them. Lady Maryam is in this group. There are many ayahs (verses) throughout the Qur'an which refer to Maryam and there is a chapter in the Qur'an revealed in Maryam's name. She is a lady with such dignified position for whose protection and taking care, the pious ones quarreled with one another. And Zakariyah, the prophet of Allah, noticing the divine attention towards this great lady and despite being old and his wife being infertile, he prayed to God to grant him a child and his prayer was answered.
4- 3. If we go through the historical reports, we come across ladies who, despite marrying oppressive and unjust rulers, maintained their faith and showed great resistance against their tyrant husbands. Asiya wife of Pharaoh can be introduced as a suitable model representing such ladies. She was harassed and tormented so much by Pharaoh that she prayed to God for death and martyrdom and she finally achieved her goal. The Quran praising the bravery and valor of this woman introduces her as a model for all faithful people irrespective of whether they are male or female.
5-3. Contrary to the above group, we find women who enjoyed the privilege to become the prophets' wives but unfortunately and to every one's dismay, they not only did not help them and thank God for this great blessing but they continuously conspired against them, hurt and annoyed them and did whatever they could to create hurdles on the way of those prophets. One of them was Noah's wife; God, the Almighty, ordered Prophet Noah, after the typhoon had just started, to load from every species of animals a couple and He forbade him from picking his wife and one of his sons who did not believe in him.
Prophet Lut's wife also ended having an evil fate as she was subjected to divine punishment along with other unbelievers.
In the last part of Sura al-Tahrim, God introduces these two women as ungrateful women who despite being married to noble and righteous people, acted treacherously towards them. Their relationship with the prophets was of no avail to them and therefore they were told to enter Hell along with other unbelievers.
It is interesting to know that at the beginning of the same short chapter i.e. Sura Al-Tahrim in which reference has been made to the evil fate of Noah and Lut's wives, two of the Holy Prophet's wives have also been reproached and reprimanded for their unfavorable and annoying behaviors towards him. They have been introduced to Islamic society as individuals whose hearts have been stained with darkness.
Regardless of how they hurt and misbehaved with the Prophet (s), there is no doubt among the historians and exegetes - Sunni and Shia – that these two women were Aisha, the daughter of the First Caliph and Hafsa, the daughter of the Second Caliph!
If you do not believe us and you think that Shiites have fabricated this story, we advise you to go through some of the most important Sunni sources to see to your amazement that they have also confirmed the same story seeing no one other than Aisha and Hafsa to be the manifestations of the aforementioned verses. We just cite only two examples of the traditions narrated in Sahih Bukhari and Sahih Muslim and leave the rest to you to study:
A) Narrated Ibn Abbas: "I intended to ask 'Umar so I said, "Who were those two ladies who tried to back each other against the Prophet?" I hardly finished my speech when he said, They were 'Aisha and Hafsa."
B) Narrated Ibn 'Abbas: I had been eager to ask 'Umar bin Al-Khattab about the two ladies from among the wives of the Prophet regarding whom Allah said 'If you two (wives of the Prophet namely Aisha and Hafsa) turn in repentance to Allah, your hearts are indeed so inclined (to oppose what the Prophet likes) till 'Umar performed the Hajj and I too, performed the Hajj along with him. (On the way) 'Umar went aside to answer the call of nature, and I also went aside along with him carrying a tumbler full of water, and when 'Umar had finished answering the call of nature, I poured water over his hands and he performed the ablution. Then I said to him, "O chief of the Believers! Who were the two ladies from among the wives of the Prophet regarding whom Allah said: 'If you two (wives of the Prophet) turn in repentance to Allah your hearts are indeed so inclined (to oppose what the Prophet likes)?" He said, "I am astonished at your question, O Ibn Abbas. They were 'Aisha and Hafsa."
Now, we want you to answer as to why God, the Exalted, speaks about the fate of another two ladies immediately after He reveals verses denouncing Aisha and Hafsa for their act of hurting the Prophet (s). Why does God speak about the fate of two women who, like Aisha and Hafsa, were the wives of prophets but their relationship to those prophets were of no avail to them?
Therefore, one cannot consider the wives of prophets as being utterly and absolutely beyond any criticism.
4. Having said that, we can now meticulously illustrate Shi'ahs' perspective about Aisha and say that she enjoys two positions according to us:
First position: Although we criticize Aisha for the reasons mentioned above, we also respect her as one of the wives of the Holy Prophet (s) and because the Quran regards the Prophet's wives as the mothers of the faithful. We respect her to the same degree that our Master, Imam Ali (a.s.) respected her following his victory in the Battle of Jamal in which Aisha pleaded Imam Ali for forgiveness and the Imam returned her to Medina with full respect and with forty armed women accompanying and guarding her.
Also, we do not accept the false accusation levied against her in the "slander" event. As stated in some Shia sources, we believe that such sins cannot be committed by a wife of the Prophet (s) and that what is mentioned in the Quran as treachery refers to other offences committed by her. Basically, we do not assail anyone by levying false accusations against him/her simply because we have some objections towards him/her. We believe such an act, as per the Quranic verse, is unjust because the Quran says that our criticism of people should not incite us to act unjustly.
Second position: We know that obeying a mother is incumbent to a limited degree determined by God. We are not allowed to obey her absolutely and under all circumstances. Unfortunately, this wife of the Prophet (s) and the Mother of the Faithful, committed acts which have given rise to objections on the part of some Shiites as well as some fair-minded Sunnis. We shall now mention only two important instances and leave the rest to you to study:
First instance: "Aisha hurt the Prophet (s) many times during the period she lived with him. As was stated in the third part of this answer, a few verses were revealed denouncing her and one another wife of the Prophet (s).
Second instance: Aisha was one of the most important individuals involved actively in the internal and well-organized civil wars ignited among Muslims. She ignored the Prophet's advice to her as we shall explain below:
During the period of the third caliph when public indignation increased against some of his designees, Aisha was one of the people who propagated heavily against him and even likened him to a Jewish man named Na'thal. She even incited people to kill him telling them "Kill the Na'thal" but when the insurgency intensified, she left Medina for Mecca thinking that as soon as Uthman would relinquish from power, her relative, Talha, who was also one of the leaders of the insurgency, would take the reign and occupy the caliphate. On her way to Mecca, she learned that Uthman had been killed. She became happy hearing the news and immediately asked the reporter as to whom the caliphate had been transferred to. When she heard that the people had chosen the Commander of the Faithful, Ali (a.s.) as the caliph, she suddenly changed her position and expressed regret over Uthman's murder! The reporter was taken aback with this sudden change of position. Therefore, he asked: "You were one of those people, who were instigating people against Uthman, how come you have now changed your opinion? Aisha answering this criticism and without denying her role in the insurgency answered: "Yes, I was among the opponents of Uthman but I believe the people must have made Uthman to repent and then they might have killed him! Then she returned to Medina and completed all preparations for the Battle of Jamal.
What was presented in this study has been extracted from Sunni sources and one cannot deny or reject them. Also, there are many other topics in the same books and also in Shi'ah sources each of which can give rise to more criticisms but we are not going to discuss them for the sake of brevity but we want you to reply to our question without any prejudgment:
What is the reason a person cannot criticize a lady who enjoyed the honor to be the wife of the greatest Prophet sent to mankind but who with her annoying the Prophet (s) caused some intimidating verses to be revealed. In addition, she played an important role in starting an internal war among Muslims because she was involved in Uthman's murder and, by ignoring the Holy Prophet's warning, she launched the "Battle of Camel" causing the blood of thousands of her children to be spilled without any specific results.
If she is beyond any criticisms simply because she is the wife of the Holy Prophet (s), then why God considers, in Sura al-Tahrim, the wives of some of the prophets as being entitled to the Fire of Hell?! Why does God, addressing the Prophet's wives, say that whoever among you commits a blatant sin will be punished twice as much as other people? Do you find a sin more blatant and open than a military surge against the Prophet's brother, his successor and the murder of thousands of people under the pretext of avenging the blood of a person in whose death she herself was primarily and overtly involved?
 - Al-Noor, 23.
 - Qurtubi, Muhammad bin Ahmad, Al-Jame' le-Ahkaam al-Qur'an, vol.13, pg. 209, Nasir Khosro Publications, Tehran, 1364 (1985).
 - Sahih Bukhari, vol.3, pg. 154 – 155, Dar al-Fikr Publication, Beirut, 1401 A.H.
 - Sahih Bukhari, vol.6, pg. 13.
 - Sahih Bukhari, vol.5, pg. 61.
 - Tabari, Abu Ja'far, Jami'ul Bayan fi Tafsir al-Qur'an, vol.18, pg. 82, under verse 22 of Sura al-Noor, Dar al-Ma'arefah Publication, Beirut, 1412 A.H.
 - Vide: Tabarsi, Fazl bin Hasan, Jawame'ul Jami', vol.3, pg.98, Tehran University Press, 1377 (1998); Tusi, Muhammad bin Hasan, Al-Tebyan fi Tafsir al-Quran, vol.7,pg. 415, Dar Ihya al-Turath al-Arabi, Beirut.
 - Ali bin Ibrahim, Tafsir Qommi, vol.2, pg. 99, Darul Kitab Institute, Qom, 1404 A.H.
 - Al-Nisa, 137; Al-Munafeqoon, 3; Al-Maedah, 54
 - Al-Tawbah, 38; Al-Maedah, 51, Al-Ahzab, 69; Al-Hojurat, 1-2; Momtahenah, 1; Al-Saf, 2; Al-Munafeqoon, 9; Al-Anfal,5.
 - Al-Furqan, 74.
 - Al-Masad, 1-5: Perish the hands of the Father of Flame! Perish he! No profit to him from all his wealth, and all his gains! Burnt soon will he be in a Fire of Blazing Flame! His wife shall carry the (crackling) wood - As fuel!- A twisted rope of palm-leaf fibre round her (own) neck!
 - Al-Tahrim, 12; Aal-e Imran, 42-43 etc.
 - Aal-e Imran, 44: "hou wast not with them when they cast lots with arrows, as to which of them should be charged with the care of Mary: Nor wast thou with them when they disputed (the point)."
 - Aal-e Imran, 37 -40: "There did Zakariya pray to his Lord; he said: My Lord! grant me from Thee good offspring; surely Thou art the Hearer of prayer."
 - Al-Tahrim, 11: "And Allah sets forth, as an example to those who believe the wife of Pharaoh: Behold she said: "O my Lord! Build for me, in nearness to Thee…"
 - Hud 40: We said: "We said: Load therein two of every kind, a pair (the male and female), and thy household, save him against whom the word hath gone forth already, and those who believe."
 - Hud, 81, "And let not any of you look back: but thy wife (will remain behind): To her will happen what happens to the people."
 - Al-Tahrim, 10: "Allah sets forth, for an example to the Unbelievers, the wife of Noah and the wife of Lut: they were (respectively) under two of our righteous servants, but they were false to their (husbands), and they profited nothing before Allah on their account, but were told: "Enter ye the Fire along with (others) that enter!"
 - Read the full story in reliable Sunni or Shi'ah Tafsir (commentary books) under Chap. Al-Tahrim.
 - Al-Tahrim, 4-6: "If ye two turn in repentance to Him, your hearts are indeed so inclined; But if ye back up each other against him, truly Allah is his Protector, and Gabriel, and (every) righteous one among those who believe,- and furthermore, the angels - will back (him) up."
 - Sahih Bukhari, vol.6, pg. 70
 - Sahih Bukhari, vol.6, pg. 147 – 148; Sahih Muslim, vol.4, pg. 192, Dar al-Fikr, Beirut.
 - Al-Ahzab, 6: "And his wives are their mothers."
 - Shakh Mufid, Al-Jamal, pg. 415, Congress on Shaykh Mufid, Qom, 1413 A.H.
 - Majlisi, Muhammad Baqir, Behar al-Anwar, vol.11, pg. 308, Al-Wafa Institute, Beirut, 1404 A.H.
 - Al-Maedah, 8: "And let not the hatred of others to you make you swerve to wrong and depart from justice."
 - Al-Ankabut, 8; Luqman, 15: "But if they strive to make thee join in worship with Me things of which thou hast no knowledge, obey them not; yet bear them company in this life with justice (and consideration)."
 - Ibn Kathir al-Demashqi, Al-Bedayah wan-Nehayah, vol.6, pg. 212, Dar al-Fikr, Beirut, 1407 A.H.
 - Tarikh al-Tabari, vol.4, pg. 458 – 459, Dar al-Turath, Beirut, 2nd edition, 1387 A.H.
 - Al-Ahzab, 30: "O wives of the prophet! whoever of you commits an open indecency, the punishment shall be increased to her doubly."