If that was to happen, I'd send any members that had left an apology on my, and the rest of the staff's, behalf and reassure the community that the matter will be taken care of. Depending on the situation with the moderator, I would suggest that they be punished for any rules they may have broken, as well as given a probationary period of some sort, depending on the severity of their actions. Afterwards, I would mainly deal with damage control, i.e. getting threads back on track, deleting any especially nasty comments, etc.
If the community starts becoming split over an issue, I would encourage members to discuss the matter as a community. Because topics can easily become arguments when many people disagree, I would be watching especially closely in order to make sure the discussion remains civil, and not directed at anyone personally (I would suggest that any members getting into an especially heated debate take the matter into a PM between themselves.). I think it's important that the community is willing to discuss what's bothering them when a problem arises, but it's also very important that the situation isn't allowed to get out of hand.