Do Muslims and Christians Worship the Same God?

Apparently this is a question that is gaining some attention recently by way of a multitude of articles posted on the Internet.  I must admit that I was not aware of such articles, until I watched (listened to, actually) this video by James White, who I always find to be edifying.  Dr. White, as usual, seems to have hit the nail right on the head, where so many of us often hit it a glancing blow resulting in a bent nail.

For the whole story, I recommend watching the 24 minute video, but here is my condensed and paraphrased version of White's points:

Historically Muslims and Christians are talking about the same God, but that is not the same as worshiping the same God. Mohamed and the Muslims say that Allah is the God of Abraham. Christians also claim to follow the God of Abraham.

The New Testament says that "the hour cometh, and now is, when the true worshippers shall worship the Father in spirit and in truth" 

However the author of the Koran seemed to believe that the Trinity worshiped by the Christians consisted of God the Father, Mary the wife and Jesus the son.  That is an excusable mistake considering that by Mohamed's day there were already local sects that had gone off the rails and were bowing down to statues of Mary (just as the church of Rome still does to this day). 

This is where the rubber meets the road.  Islam denies that God has a son.  Christianity confirms what is revealed about the deity of Christ in the Bible.  The Koran would seem to equate worshiping Jesus as God with an unforgivable sin.   If God is who the New Testament reveals him to be, then those who deny the Trinity cannot be true worshippers.  Likewise, if the New Testament is wrong and the Koran correct, then Christians cannot be worshipping in truth.  I must add though, it does seem a little strange that if "Allah" was going to correct the record about a Trinity that the Christians were mistakenly worshipping, he wouldn't have "clued in" his prophet as to the actual identity of the members of the Trinity.