We believe that the Quran enjoys comprehensiveness and is capable of solving all problems of people's lives, but such a claim does not mean we should expect the Quran to solve everything, even the problems of physics, etc.
The Holy Quran is a book of guidance for all people and this is the sole purpose for its revelation, consequently we should only expect it to be exhaustive in this field. In other words the Quran should not neglect mentioning any point that is required for the people's guidance. Of course we believe that the Quran has carried out this responsibility and has mentioned all of that people need for guidance and has solved people's problems in this field. But we must keep in mind that religion is only responsible of explaining issues that people cannot understand or unveil on their own. Allah has granted the human being mind, intellect and thought and religion is definitely not aiming to take away these abilities, because this would mean that physical senses, intellect and human experience were all created in vain. In this regard Question 900 (The theory of codified thought in Islam [website: 988]) can answer part of your question.
We must note that since the Quran is a book of guidance it does not differ from other holy books and is similar to them, the sole difference is that the Quran is greater than them and more comprehensive.
I must thank you for posing your question on this site in order to reach the truth and giving us the honor to answer your question. Taking some points in to consideration can help us reach the answer:
1- We believe that the Quran enjoys comprehensiveness, but such a claim does not mean we should expect the Quran to solve every single problem.
Even though there have been divergent understandings regarding the comprehensiveness of the Quran among Muslim scholars, but most of them understand it as an exhaustiveness that leads to fulfilling the aims of religion and believe that the comprehensiveness of the Quran is defined within this field.
The Holy Quran is a book of guidance for all people and this is the sole purpose for its revelation. Therefore everything that is related to guidance is mentioned in it, whether it is truths pertaining to the genesis of this world, the Hereafter, ethical virtues, parables, rulings or admonitions that people need in order to find the right path. We must keep in mind that religion is only responsible for explaining issues that people cannot understand or unveil on their own. In fact, the Holy Quran and generally Islam are not supposed to interfere in fields of knowledge that people can discover by themselves, because Allah has granted the human being mind, intellect and thought and religion is definitely not aiming to take away these abilities of mankind, because this would mean that physical senses, intellect and human experience were created in vain. The Quran's primary teaching is understanding Allah and has deemed belief in the one God as the cornerstone of faith. After introducing Allah, understanding the Hereafter (believing in the Day of Judgment in which each person receives the rewards or punishments of his good or evil actions) is derived from it and it is considered another principle of faith. Subsequently understanding the Messengers of Allah is derived from understanding the Hereafter; because one is not rewarded or punished for his good or evil deeds prior to being informed of what acts are prohibited or obligatory through revelation and messengers. This too is considered another principle of faith, and as a result the Quran mentions the belief in one god, the belief in prophets and the belief in the Hereafter as the Usul al-Din (Fundamental Beliefs) of Islamic faith.
After that, it has explained the virtues and ethical features which are compatible with the three fundamental principles of faith that a believer must possess. Then it has mentioned and explained the practical rules that lead to true prosperity and salvation and helps one develop and enhance his ethical virtues, and greatest of all, develop the true beliefs of faith. Virtues are enhanced by a set of proper acts and conducts, and virtues do the same for fundamental beliefs; For example if one is proud, self-centered, selfish and egoistic, we should not expect him to believe in Allah and show humility for his Lord. Also one who has not understood fairness, care, compassion and mercy his whole life can not believe in the Day of Judgment.
The Holy Quran fulfills man’s purpose of creation and does so in the most comprehensive way; because the aim of humanity, which is intertwined with realism, is one’s world view which necessitates carrying out the proper ethical principles and practical laws, and the Quran has assumed the responsibility of explaining these teachings in detail. When describing the Quran, the Almighty says: "یهدى الى الحق و الى طریق مستقیم" "It guides to the truth (in belief) and to a straight path (in practice)."
2- The Quran does not differ from other holy books and is similar to them in terms of being a book of guidance; the only difference is that the Quran is greater than them.
In other words the Quran consists of the meaning of all previous holy books and everything that people are in need of to reach prosperity and salvation in the two fields of belief and practice. From the Quran's point of view the true religion and faith was the same from the time of Adam up until the time of Muhammad. All Prophets, whether they were presenting a new religion or preaching the teachings of previous ones, have called humanity to the same ideology and faith. The Quran stresses this fact and says: " شرع لکم من الدین ماوصى به نوحاً و الذى اوحینا الیک و ما وصینا به ابراهیم و موسى و عیسى"
"He has prescribed for you the religion which He had enjoined upon Noah and which We have [also] revealed to you, and which We had enjoined upon Abraham, Moses and Jesus"
The slight differences between holy religions are as follows:
A: Holy religions differed in a set of secondary issues that were dependant on time, circumstances, the environment and people's features. In other words they were all different shapes and parts of one truth and fulfilled the same goal.
B: As man's intellect progressed and developed, ensuing prophets presented their teachings, which were all in the same field, at a higher level.
This is the progression of religion, not the differing of religion, and this is why the previous prophets had glad tidings for the coming of next prophets while they would approve of and believe in the previous ones.
The Quran says: " و انزلنا الیک الکتاب بالحق مصدقاً لما بین یدیه من الکتاب و مهیمناً علیه " " We have sent down to you the Book with the truth, confirming what was before it of the Book and as a guardian over it."
The word "مهیمن" means a guardian and keeper and the Quran being "Moheimen" over other holy books means:
First: The Quran maintains them and confirms their (holy books') truths.
Second: It protects them and is a guardian over them and mentions all the mistakes, distortions and alterations that have made their way into them. This correction is definitely not limited to the field of practical rulings and Ahkam but it also covers fundamental beliefs.
 Therefore when it is said that Islam is a comprehensive religion, it is not meant that it has mentioned the answer to all intellectual and practical problems in people's physical and spiritual lives, not detailed issues and not even regarding general issues. Instead what is meant is that it has not even neglected mentioning one point that pertains to its purpose and aim which is to guide mankind to its true and comprehensive perfection.
But we must keep in mind that religion can have to aims:
A: A permanent and continuous aim which is not related to a specific period of history or geographical region (Primary aim): Guiding the intellect and physical senses of humans (to show the path to intellectual and physical/empirical knowledge) and completing people's knowledge (creating new horizons of truths and knowledge that people can not discover on there own) are the two permanent aims of religion and in these two fields people are always in need of religion.
B: Temporary aim (Secondary aim): Mentioning certain solutions for specific environmental or historical situations and explaining several intellectual and scientific issues during certain periods of time and for a special group of people.
Obviously when the situation, time and place changes, those solutions will no longer do people any good and because it is not considered a permanent aim for religion, that solution should not be emphasized on. Religion is not aiming to disable man's intellect and thought, and it is not religion's responsibility to present revelations as a substitute for intellect. Instead the aim of religion is to First: Guide mankind in the path of reaching intellectual and empirical knowledge, Second: creating new horizons of truths and knowledge that mankind can not discover on its own. On this basis, in regard to the permanent aims we should refer to religion and in regard to the temporary aims we should refer to our intellect and physical senses.
The special mechanism that lies in the legislating system of Islam and has the ability to reconcile between the changing and permanent aspects of human life, is comprised of five elements which are as follows: 1- The primary and secondary Ahkam 2- The establishment of Ijtihad in Islam 3- The key role of intellect in Ijtihad 4- The purposes of Akham and the rule of Ahamm (more important) and Muhmm (important) 5- The responsibilities and authorities of the Muslim Leader.
 See: Tabatabai, Muhammad Husein, Al-Mizan fi Tafsir al-Quran, vol. 12, pg. 347.
 Ma’refat, Muhammad Hadi, Jame’iyyate Qurane Karim Nesbat beh Ulum va Ma’arefe Bashari, “Nameye Mofid” Quarterly Journal, issue 6, pg. 6.
 Ma’refat, Muhammad Hadi, “Naqd va Nazar” Quarterly Journal, issue 1, pp. 63-64.
 In regard to the connection that true beliefs and ethical virtues have with practice, the Almighty says: "إلیه یصعد الکلم الطیب و العمل الصالح یرفعه" Fater:10. "To Him do ascend the good words; and the good deeds, lift them up."; And regarding the link between belief and practice He says: " ثم کان عاقبة الذین اساؤا السوآى ان کذبوا بآیات الله و کانوا بها یستهزؤن " Rum, 10; "Then the fate of those who committed misdeeds was that they denied the signs of Allah and they used to deride them."
 Tabatabai, Muhammad Husein, Al-Mizan fi Tafsir al-Quran, vol. 15, pg. 47.
 … ; In this regard the renowned Shia Jurist, Kasheful-Ghita says: "If it was not for the prophet and the Quran, no such thing as Christianity and Judaism would have existed today; because the distorted Torah and Bible that claim Allah wrestled and competed with Ya'qoob, the prophets consumed alcohol and accuse pious women of sexual misbehavior would have not had the ability to remain as holy books. Along with promoting and preaching Monotheism, the Quran has also exonerated all prophets from such accusations and has greatly hailed Ibrahim and the other prophets and mentioned the Virgin Mary as a figure of piety and righteousness. The Holy Quran also corrected the distortions that had made their way in to the books of previous prophets… In addition to correcting fundamental distortions of holy books, the Quran also corrected distortions that were made in the Furu' Din (Branches of Religion)."