The book that the pope appears to be kissing looks like no Qur'an I have ever seen. The symbol on the cover is enough like that on the cover of my own copy of the Qur'an (no I am not a Muslim), but does not seem to be identifiably Islamic. The problem with identity is that the 'book' looks more like a binder or outer cover - when you zoom in, it seems to be enclosed on both edges, whereas a Qur'an is not normally presented in this way. It may be that Pope St. John Paul II was simply following traditional Arabic custom by kissing a gift presented to him, whatever was held in that binder. Nevertheless at least one website claims authenticity for the event:
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.
The question becomes one of whether it is appropriate for the pope to show respect for members of another religion and for its holy book. The Second Vatican Council issued, in 1965, Pastoral Constitution On The Church In The Modern World. Part I, chapter II (28) states:
Respect and love ought to be extended also to those who think or act
differently than we do in social, political and even religious
matters. In fact, the more deeply we come to understand their ways of
thinking through such courtesy and love, the more easily will we be
able to enter into dialogue with them. [My emphasis]
Either way, it appears the Vatican has not seen it necessary to post an explanation of the photograph. I think we should give the pope the benefit of the doubt and believe that he acted with propriety and sensitivity to the feelings of the Catholic community he leads.