He cheated on both of his previous wives. Usually when politicians in US do something like this they have to resign. However this appears to be a very one-sided thing because 'complete transformation by God' seems to be at the core of the evangelical worldview (even though Gingrich I believe is catholic, the vast majority of the voters are protestant). If it's a liberal politician they are automatically denied the repentance/redemption narrative, if it's a conservative they're automatically granted it.

How much of a jerk he is beyond cheating on his wives probably doesn't matter all that much. In fact a lot of the partisan voters want their guy to be a jerk, so that he can take on and destroy the opposing side.

I have some friends from the south who are telling me that it would be next to impossible to get a mormon elected. It may be true, I've heard many times that the south turned from democratic to republican over the civil rights.