Continuing with some notes on the topic:
Islam and Mormonism conceive of God rather differently. Mormonism teaches an embodied God; at least officially (whatever ordinary, uneducated Muslims may believe, and though the Qur’an can easily—and, I think, should—be read otherwise), Islam teaches of a God without body or location. (There is overwhelming evidence that many early Muslims, probably including the Prophet Muhammad himself, believed in a corporeal deity.)
The line of prophets in Islam culminates with Muhammad, and the overwhelming majority of Muslims do not believe that any prophet can or will come after Muhammad. Mormonism has never recognized Muhammad as a prophet (though some Church leaders have been willing to describe him as inspired), but affirms the post-biblical prophethood of Joseph Smith and a line of successors.
The unforgivable sin in Islam is shirk. (The Arabic word means, roughly, “association,” but can be loosely rendered as “polytheism.”) To commit shirk is to worship or recognize any other deity beyond or instead of the one true God. Muslims are uneasy with the mainstream Christian view of the Trinity, despite Trinitarian protests that the Trinity is really just one God; they will, I think, tend to find Latter-day Saint references to “the Gods” (as in the Book of Abraham and elsewhere) rather disturbing. I see this as a potential flashpoint in our relations with Muslims. (However, historically, Muslims have learned to live more or less in peace with Hindus and other undeniably polytheistic groups, and even to evolve ingenious ways of considering them “actually” monotheists, so this can probably be managed. There is, obviously, as the Book of Mormon makes clear, a very powerful sense in which we too can truthfully say that we worship and believe in only one God. This will need to be emphasized in any theological discussions with devout Muslims, when and if they arise.)
Crucial difference: Islam recognizes Jesus as a prophet, even a very great one, but only as a prophet. He is not the Son of God, for Islam recognizes no children of God. Qur’an 112 reads as follows: “Say: He is God, One. God, the Absolute. He does not beget nor is He begotten, and there is none like unto him.” (It is just remotely possible that Muhammad is not responsible for this passage. But I know of no way to prove it, and he probably was.)
While both Mormonism and Islam speak of the Virgin Birth of Jesus, Latter-day Saints do so to insist that Jesus’ father was not Joseph but God himself, with all that that entails for Jesus’ capacity to save us in his role as Savior and Redeemer. Muslims, by contrast, insist that Jesus was the “son of Mary.” He had no father at all, but was a miraculous sign from the all-powerful God.
To be continued.