Do Muslims and Christians worship the same God?

A most interesting analysis by Robert Spencer at Crisis Magazine:

I

t certainly seems as if we worship the same God. After all, we call God by the same name. Arabic-speaking Christians, including Eastern Catholics such as Maronites and Melkites, use the word “Allah” for the God of the Bible.
But are they the same God?
The question is not answered by simple linguistic identity, as evidenced by St. Paul’s complaint to the Corinthians: “For if some one comes and preaches another Jesus than the one we preached, or if you receive a different spirit from the one you received, or if you accept a different gospel from the one you accepted, you submit to it readily enough” (2 Corinthians 11:4). The “other Jesus” that was being preached among the Corinthians was not a different person of the same name, but a view of Jesus of Nazareth that was so radically different from Paul’s that he termed it “another Jesus” altogether.
In the same way, it is possible that the Qur’an and Islamic tradition present a picture of God so radically different from that of the Bible and Catholic tradition that it would be difficult, if not impossible, to maintain the proposition that they are the same Being in both traditions, apart from some minor creedal differences.
But wait a minute. Don’t Catholics have to believe that Christians and Muslims worship the same God, because the Second Vatican Council says so? The Dogmatic Constitution on the Church tells us that the “plan of salvation also includes those who acknowledge the Creator. In the first place amongst these there are the Mohammedans, who, professing to hold the faith of Abraham, along with us adore the one and merciful God, who on the last day will judge mankind.” (Lumen Gentium 16)