Creed 2:6 and Acts 17 are two closely related ministries of Christian apologetics to muslims and interested Christians. In their web pages you can find links to good and respectful debates between Christian and Muslim apologists. If you don't know about Islam, you can go to the 101 very good introduction by Qureshi in Creed 2:6 or follow some of the links of Acts17 to the Muslim side.
I have come to learn some things though:
1) I didn't realise that the standard defense of the Quran was so falsifiable. Islamic standard apologetics says that Quran has predictions of science that was unkonwn at that time, which proves that the Quran was revealed. I have leaflets given to me by muslims in Portsmouth that stress this particular point a lot.
However I found that unsound. I am linking here (where you can find a pdf) to a refutation of the embriology science from the Quran. See a debate here where the Quran is (allegedly) shown to have proof of last astronomical discoveries.
2) I also didn't realise that compared to the New Testament the Quran is a a violent book, from which it is possible that that Islam should be imposed to the unbelievers (not that all muslims agree, of course, see for instance the debate below for the two views).
Another debate. Who was Jesus? I like the debate below where this is discussed. I like a lot both speakers, even if I disagree with the penal substution soteriology of Qureshi, and with the Islamic view of Hashim. This debate may be used as an example of a good and respecful discussion of both Christianity and Islam. This is the 2nd of 3rd parts, you should watch all the debate though.
Finally a link to intereligeous dialogue for mutual understanding and harmony here, and to a youtube channel on Christian and Muslim debates here.