Is the Qur'an compatible with Christianity? In comment discussion of another question, these mentions about the Qur'an were made:


  The Qur'an teaches that Christ is a Prophet in Islam. In that sense I wouldn't say it's "Anti-Christian" or even heretical.
  
  I merely made this distinction because it doesn't directly teach against Christian theology, and some Christians have a similar view to the Qur'an with respect to the divinity of Christ.


I had never before heard of Christians that see the Qur'an as compatible with Christianity. I think this has a lot to do with what doctrines a Christian holds onto. For the purpose of this question, anyone self-identifying as a Christian is a Christian.


What Christian doctrines is the Qur'an incompatible with?
Is the Qur'an generally compatible with Christianity? (i.e. other than being incompatible with the specific doctrines)
No, it is not compatible. The Qur'an explicitly denies the divinity of Christ, which is one of the absolute bedrock tenets of the Christian faith. Without His divinity and associated sinlessness Christ's sacrifice and resurrection would carry no meaning or effect.

One additional note: I ran across this article today and I thought it would round out this answer well. In it the author explains the doctrine of the Trinity and why it matters so much. The fact that Christ was divine and one part of a triune Godhead is critical to Christianity, and as I said the Qur'an denies it outright. A great summary of the Trinity from the article:


  The doctrine of the Trinity can be summarized in seven statements. (1)
  There is only one God. (2) The Father is God. (3) The Son is God. (4)
  The Holy Spirit is God. (5) The Father is not the Son. (6) The Son is
  the not the Holy Spirit. (7) The Holy Spirit is not the Father. All of
  the creedal formulations and theological jargon and philosophical
  apologetics have to do with safeguarding each one of these statements
  and doing so without denying any of the other six.


Without a Trinity there is no Christianity, therein lies the direct conflict with the Qur'an.