To avoid wasting time skimming my massive "wall of logic" above, one could simply read this bit of Akwat's post, which pretty much covers everything valid in this discussion:

It's not quite that simple, though. Islam does not teach that Christians, Jews, and Muslims all worship the same God. Rather, it holds that Allah is the only true and living God to which the Jewish and Christian Scriptures originally testified. However, those Scriptures have become corrupted over time and therefore by the time of Muhammad were no longer to be considered completely reliable. Just as Joseph Smith's angelic vision is held by Mormons to signal the restoration of doctrinal truth, so also Muhammad's angelic vision is held by Muslims to signal the restoration of doctrinal truth. This is the Islamic doctrine of abrogation: where the Old and New Testaments err, the Qu'ran and Hadith correct them--and one of the most egregious errors in Jewish and Christian Scripture, according to Islamic teaching, is the departure from belief in Allah and the concomitant advocacy of false gods (Yahweh/Jehovah, Jesus, the Holy Spirit, etc.). The only way that Jews or Christians may come to worship the true God to whom their Scriptures originally pointed, is by converting to Islam. That's why the Islamic version of hell contains two levels reserved for the everlasting punishment of Jews and Christians (Al-Hut?amah and Laz?a respectively; cf. Dictionary of Islam, edited by Thomas Patrick Hughes [Clifton: Reference Book Pub., 1965], 171.)