What Candy Crowley did in 2012 is really disqualifying. Fact-Checking is for the other candidate to do or for the media to do AFTER THE DEBATE. As the moderator, your job is to ask questions and keep a hold on answer time. Your job is not to try to "gotcha" a given candidate. And I don't care that Crowley said a sentence favorable to Romney right after the one that was favorable to Obama, because the one that was favorable to Obama was what everyone actually remembered.
It wasn't a "gotcha" give me a break. Romney tried pushing the republican talking point that Obama didn't call it an act of terror, but he so clearly did, and then Obama responded with the famous "Please proceed, Governor" and Romney deservedly looked like a fool.