This issue is foundational to Islam
An essential argument for the Muslim faith is the perfect preservation of the Koran. Every word, every letter, every feature of the Koran must remain exactly as it was revealed from Allah to Muhammad, and also Muhammad to our days. It is an essential belief because of the Islamic view of the Koran. For Islam, it is the eternal expression of Allah, therefore it can never be subject to any change or corruption. Its immutability is also a necessity because it is the foundation of Sharia, a law for all times.
It is argued that the proof of the miraculous inspiration of the Koran is prophesied in the Koran itself: “We have certainly revealed the warning (that is, the Koran,) and we will certainly be its guardian” (15: 9). Since Muslims believe that all other sacred books have been corrupted by their followers, this miracle is all the more powerful in their eyes.
ANSWER: HOW DO THEY SAY IT WAS PERFECTLY PRESERVED?
Although Muslims have a firm faith in the perfect preservation of the Koran, it is impossible to prove it. When Othman produced an official copy of the Koran and destroyed all the other copies, he left no way for future historians to determine whether the Koran we have today really dates back to Muhammad. Othman has destroyed all the evidence.
If the copies were all identical, why were perfect copies all destroyed?
Why did he feel the need to destroy all the other existing copies of the Koran if they were all exactly identical with the one he preserved? If anyone burned a copy of the Koran today, there would certainly be protest, if not violent reaction. It must therefore be that he did it, precisely because there were variants and corruptions being copied and distributed.
It cannot be proven or disputed because there are no other copies from before that time.
Although perfect preservation can not be proved, it can be refuted to some extent. In the first place, the Koranic text has not always been written, but sometimes only memorized. It is for this reason that Omar convinced Abu Bakr to first gather a copy of the Koran. Many Qari, (the reciters of the Qur’an,) were on the battlefield, and Omar said, “I fear there will be a great number of victims among the Qari on the battlefields, (they represent) a large part of the Koran.  If the Koran had already been written in its entirety, as some Muslims claim, why would they fear its loss by the death of the reciter?
Was it written?
The fact is that certain portions of the Koran had not been written, and that it was necessary to gather the missing parts from the recollection of the reciter. This is said explicitly in Sahih Bukhari: The Quran was gathered from “stalks of palm trees, fine white stones and also from those who knew it by heart.” The same Hadith tells us that at least two verses were known by only one person: “I went in search of the Koran until I found the last two verses of Surat at-Tauba with Abi Khuza’ima Al-Ansari and I could not find the verses with anyone other than him.  In other words, two verses of the Koran were included on the testimony of a single individual. If he had not remembered these verses, they would have been lost, and we would not have been wiser.
One verse was admittedly missed out in the first edition of the Koran
Sahih Bukhari mentions that a verse had been lost in the first edition of the Koran, and that it was necessary to find it afterwards: “When we copied the Koran, I omitted a verse from the Surah Ahzab, verse which I used to hear recited by the Messenger of Allah. We sought it, and found it, with Khuza’ima bin Thabit Al-Ansari. 
It seems that whole verses have been forgotten and lost, and it is with great difficulty that it was recovered.
Muhammad himself used to say that Muslims tend to forget the Koranic verses very easily. “Never stop reciting the Qur’an because it escapes from the hearts of men faster than a camel.  He did not exaggerate, for he himself forgot certain verses. One night, as he heard a man recite the Koran, he declared, “May God grant him his mercy, just as he did for me by remembering certain verses I had forgotten.”
If, according to the most trustworthy traditions, certain parts of the Koran were known to only one person, and other parts had been forgotten – and it is a fact that Muslims forgot verses – is it not legitimate to think that certain parts of the Koran have been omitted? Can we really say that such a precarious text has been perfectly preserved?
We cannot say it with any assurance at all. Sahih Bukhari puts the nail in the coffin of this idea, recalling the Hadith where Omar says: “Ubay was the best among us in reciting the Koran, however, we leave aside parts of what he recites,” Ubay, for his part, declared: “I have it from the very mouth of the Messenger of Allah and I will not forget absolutely nothing. In other words, he tells us that he is sure to forget some things!
Therefore, the best reciter of the Koran in person considered it certain that verses of the Koran were lost. Mohammed himself named Ubay as one of the best teachers of the Koran,  and yet he did not quote his Koran from memory in a way that agrees with the Koran which is now in our possession.
In short, it is not only impossible to prove that the Koran has been perfectly preserved, but on the contrary, it seems to have been proved that it is not reliable. One of the greatest masters of the Koran, commended by Muhammad himself, disagrees with the version of the Koran that we have today.
There is still much to be said against the argument of the perfect preservation, but this is limited to some, but by no means all, of the evidence set forth in Sahih Bukhari.
For reference: Sahih Al Bukhari available here
 Sahih Bukhari 6.61.509
 Sahih Bukhari 6.61.511
 Sahih Bukhari 6.61.510
 Sahih Bukhari 6.61.550
 Sahih Bukhari 6.61.558
 Sahih Bukhari 6.61.527
 Sahih Bukhari 6.61.521