For the Koran to be the inerrant word of god, its claims have to hold true 100% of the time. If exceptions are found, it would clearly refute its claims of divine origins. One interesting way to examine the accuracy of the Koran is with verse 8:65.
In 8:65, the Koran says this:
8.65 O Prophet! Urge the believers to war; if there are twenty patient ones of you they shall overcome two hundred, and if there are a hundred of you they shall overcome a thousand of those who disbelieve, because they are a people who do not understand.
Before looking at the accuracy of this, it is interesting to examine the tone. It does seem odd that the creator of humanity would want to urge people to war. If history has taught anything, it is that people are all too eager to go to war and fight. Any god that created people would surely know that. When then, is Allah appealing to the part of human nature that most would like to see less of? It would seem more thoughtful for any god to be telling his followers that they should be refraining from war. While the need for self defense can be argued, those words are not mentioned.
Besides, if a being with the power to create the universe needed an enemy defeated, why would he not just do it himself? Allah should be able to destroy the earth and a lot more with the blink of an eye. Therefore, it should be no problem at all destroy any kind of enemy Muslims would face with total ease or at the very least make it impossible for those enemies to wage war. It seems that would be a better way to do things than tell people to fight.
Putting all of these potential contradictions aside, does the verse make sense and hold true? It does say that the faithful will triumph, even when outnumbered. However, it is clear from the most basic examination of history that Muslims have not always triumphed. In fact, they have lost a great many battles.
In some of these battles, Muslims were the smaller force, and in others, they were the larger force. This most obvious example of the later was the battles with Israel. Israel has always faced enemies far more numerous than itself. However, when facing these Muslim enemies, it has not only held out, but often triumphed in very dramatic ways.
In addition, there has never been any hard evidence that Muslims (or followers of any religion) have ever had god on their side in any battle or war. Sure, followers or religions have sometimes gained dramatic upsets, but this has happened in many times since the beginnings of warfare. While perhaps belief can sometimes bring a fatalism that may be advantageous in battle, there is no hard evidence of a direct hand of any god in any conflict.
Some Muslims have attributed their defeats to their not following Islam properly. However, what exactly they should be doing to get divine favor back on their side can never be concretely laid out. Even if Muslims are not following Islam the way they should be, they still should be closer to this supposed divine will than their non-Islamic enemies. Would not Allah at least favor them more than non-Muslims? If Muslims are doing something they should not why would he not just tell them directly instead of letting them suffer humiliating defeats that make his own words look wrong?
Of course, this is just one verse of the Quran. Any book should be taken in its entirety. However, when looking at 8:65, there does not seem to be a basis to argue that the book is perfect in its teachings or in how the world really works. There is no hard evidence of any god ever directly involving himself in the outcomes of any battles, let alone always favoring a certain side.
Science in the Quran examines apparent flaws in the Quran in much greater detail.