Before criticizing any book, one should read it and get to know it.
However, the Qur'an is not an easy book to understand.
A Topical Study of the Qur'an is a helpful starting point to get an overview on its major topics.
The Muslim claims about the Qur'an concentrate around the topics of
Comparing the best arguments for Christianity and Islam:
The Resurrection Versus the Qur’an In the Light of Logic
Further issues in need to be investigated are
Muslim arguments and presentations:
Answering Islam Home Page