When the Muslim cannot respond to such a claim they tend to employ the Red Herring Fallacy.
A red herring is an argument, given in reply, that does not address the original issue. Critically, a red herring is a deliberate attempt to change the subject or divert the argument. 
Their usual Red Herring, if they choose to stick on topic of the Quran instead of digressing to an attack on the Bible, is in regard to the variant readings of the Quran. These variant occur with the addition of vowelisations etc for professionalised recitations to the original Uthmanic text. Now, these variant readings do not usually change the meaning of the Quran and the Muslim will give you the blanket statement that there are no differences in the Quran as a result of these variants. But is this statement true?
In regard to the variant recitations, Professor James A. Bellamy states:
These variants, however - I have counted more than two-hundred that make a difference in the meaning - are important in that they tell us there was no solid oral tradition stemming directly from the prophet to prove which variant was correct. So, we can see that there are many variants among the readings and Bellamy has recorded over 200 which render a different meaning withing the text. Professor Bellamy then goes on to provide an example:
in Surah 6:63, of the seven readers, the two from Kufah recite 'njyn' (anjana) "he saves us." and the other five 'njytn' (anjay- tana) "you (sg.) save us." These two words sound so dif- ferent that no one, unless he were deaf, could mistake one for the other, and the words on both sides of the word in question are unambiguous. One cannot argue that the prophet used one variant one day and the other the next. Nor can one maintain that there is a firm oral tradition that guarantees the reading of the unambiguous words but breaks down when more than one reading is possible. 
In short - beware of taking Muslim claims in regard to the integrity of the Quran at face value. As has been demonstrated above, there are a number of changes in meaning that result from the variant readings of the Quran. I do recommend the article for further reference purposes and it is available on the JSTOR database. If you do not have access to it leave a comment with your email address and I will send a copy your way.
2. Bellamy, p. 1
3. Bellamy, p.2
James A. Bellamy (2001), 'Textual Criticism of the Koran'. Journal of the American Oriental Society. Vol. 121 No. 1 (Jan-Mar. 2001), pp. 1-6.