According to Catholic World News, JP2 did kiss the Koran:
“At the end of the audience the Pope bowed to the Muslim holy book, the Qu’ran, presented to him by the delegation, and he kissed it as a sign of respect. The photo of that gesture has been shown repeatedly on Iraqi television and it demonstrates that the Pope is not only aware of the suffering of the Iraqi people, he has also great respect for Islam.”
http://www.catholicculture.org/news/features/index.cfm?recnum=10415
This is one of the many reasons I am glad that the JP2 cause for sainthood seems to have hit a snag.
details here;