Mitt Romney is, of course, a Mormon. People are already starting to handicap his chances with the evangelical voter bloc, given that many evangelicals object to the LDS' position on the trinity. Others, including the Pandagon folks above-cited, worry about the Church's public declarations about social issues.
I'm going to continue muttering across the fold.
The religious debate over Romney's LDS affiliation isn't really comparable with the JFK debate or the Lieberman debate. From what I've heard, even since the Papal infallability claim was issued, it's been used very sparingly, and from what I understand, there's no single voice of Judiac faith. That is emphatically not the case in the Mormon church.
In the Mormon church, an official, publicized statement from the President of the Church (often phrased "The First Presidency," which would then include the President and his two closest advisors) bears the weight of The Word of God. That's what latter-day revelation means.
I don't know what kind of long-term game the Church is playing by allowing Harry Reid and Mitt Romney to claim the religion on such opposite political sides, but I suspect that the mainstream attention to a politically divided identity will help to legitimize the religion, which of course would serve the Church's interests. (Brother Brigham once assigned party affiliation to colonies in order to diffuse non-LDS fears about Mormon national political aspirations.)
But in the context of a national campaign, it would be eminently fair to ask Romney about the LDS social agenda. LDS activists were crucial in defeating the ERA. LDS Californians spoke out from the pulpit for defining marriage as a union between a man and a woman. (This last one really rankles; a cousin heard such a pronouncement and then attended the funeral of a young, devout, gay man who gave up hope that his desires could ever be unsinful.) How much space can Romney actually create for himself between the pronouncements from Utah and his status as a believer?
What's the status on Romney's temple recommend? This is one of the base-line judgment of an LDS-member's obedience. In order to qualify for a temple-recommend, one has to undergo a fairly intrusive interview by one's higher-ups. Retraction of a temple-recommend is often used as punishment within the Church; sometimes the retracting cause will be personal. It's more likely than not that Romney's recommend is in order, but if not--well, there's a story to be investigated.
Earlier speculations on a Mormon presidency: here.