Muslims believe that Allah is the author of the Quran, yet the first surah (Fatihah, The Opening) is clearly a prayer addressed to Allah.
Other passages which could not have been authored by Allah:
Proofs have come unto you from your Lord, so whoso seeth, it is for his own good, and whoso is blind is blind to his own hurt. And I am not a keeper over you. 6:104
Shall I seek other than Allah for judge, when He it is Who hath revealed unto you (this) Scripture, fully explained? Those unto whom We gave the Scripture (aforetime) know that it is revealed from thy Lord in truth. So be not thou (O Muhammad) of the waverers. 6:114
There is not one of us but hath his known position. Lo! we, even we are they who set the ranks, Lo! we, even we are they who hymn His praise. 37:164-6
Therefor flee unto Allah; lo! I am a plain warner unto you from him. 51:50