Slippery Slope: They were talking about weapons in Syria.

Ad Nauseam: Obama and Romney both were repeating themselves the whole time to get their different points across.

Ad Hominem: Romney attacked Obama saying that he didn't travel to Israel when he visited the Middle East which I thought was irrelevant to what Obama was saying
Post hac ergo propter hoc: guns for security:

Ad Numeron: Obama and Romney both kept referring to numbers to support their points. 

Circular in Demonstrando: In the beginning of the debate Obama and Romney kept going back and forth discussing Iraq

Argumentum ad antiquitatum: Obama said that the military has always been that way, we dont need it