The one big one would be an unwillingness to submit to authority (lack of humility, desire to be obedient, etc.). If they can't be a good "under shepherd" and lead knowing they are caring for someone else's sheep, there's going to be some big problems down the line.

Good point, Andy.  I guess I should have phrased my question differently.  Here's what I meant:
Are there certain sins that, if a person has struggled with them in the past (or still battles, though doesn't give into them now), would preclude them from leading a group?  

I have run into that a little, where a person feels that their past struggles will keep them from ever leading a group.

I would think they would be the type of sins that could preclude anyone from leadership in general in a church setting. For instance, if a small group leader were cheating on his wife, that would be grounds for removal from his leadership position, until such time that individual stopped that activity, repented, and began a process of restoration within the church family (what that process looks like will probably vary from church-to-church). At such time that the process is deemed complete (presumably by the church elders or other appropriate oversight) then that person may be reconsidered for small group leadership.