Seminole,
There is more evidence to believe in the accurate compilation of Quran.
1) The learned Arabs of the time were exhaustive in their memorization. They would memorize lengthy narratives with little to no errors. Actually anthropologists have proven that before the invention of cheap paper & printing press most nations around the world tried to excel in the skill of memorization.
2) During the revelation of the Quran there were companions of the Holy Prophet who would do nothing learn Islamic conjunctions and memorize Quran! They were called Ashab-e-Suffa.
3) During the month of Ramadan, it was a tradition to recite all the Quran that has been revealed. If you are familiar with the Muslim prayers style you would know that the leader (or Imam) recits the verses of Quran loudly while the rest follow silently repeating the verses in their heart. This practice help memorize Quran to the people who are listening but if someone already knows, it's a way of correcting mistakes. Praying in such a manner 5 times a day, 365 times a year, makes the verses in-grained in the brain like second nature. Keeping in mind the fact that the Holy Prophet used to be present to make corrections is another plus.
My father leads my family in prayers everyday & he is particularly fond of some verses in Quran that he recites in prayers often. Now if someone just tells me the first few words of those verses, I can take it on from there, reciting the rest of them. Even though I don't know where exactly they are in the Quran. But just by listening to them over and over again, I have got them memorized.
4) When Hazrat Usman (The Caliph who first compiled Quran in a form of book) took up this task, he had people from all over Arabia, from all the different tribes, come over to help in the compilation! There are traditions that state that there were differences in opinion on when the verse was revealed & the pronunciation of certain words, but the content was not challenged even once! He declared that as the Holy Prophet was from the Quraish tribe, so the pronunciation of his tribe will be considered valid. (In Arabic, the same word if pronounced differently means different things).
5) It's been close to 1400 years, though not even a single evidence suggests that the original text compiled by Hazrat Usman has changed. You will find different translations, different interpretations but the Arabic text has been preserved for ever. There is only one version of Quran. If there were mistakes in the compilation, different versions are bound to pop up, but no such X copy exists.
But if one does not believe in it's divinity of a scripture then the accuracy of compilation really doesn't mean anything.