A couple of things that annoy me (mostly online related).
People who think they have you stumped with an argument that has been refuted ad nauseum. Especially when they talk to you like you're a total idiot and they are the smartest person around. Or even more annoying is someone who too literal minded to understand what the person is saying. I remember reading an FSTDT related post responding to some objections to Christianity. One of them was biblegods obsession with blood sacrifice, which is a good point. Why do people need to be brutally tortured and killed over some human fallings? Well Mr Smug Snake apologist made some insane leap saying that the OP must have trouble with the American Red Cross since that blood sacrifice saves peoples lives. It was made 10 times more infuriating by his overly condescending holier than thou attitude.
On the reverse side, there are those who read too much into someone's off hand comment. Example, I once made a sarcastic comment about how America wasn't a free country with people being arrested for weed and I got lectured about how since I wasn't shot dead for saying what I said, I should be happy to live in America. Well yeah, living in America is better than somewhere like Iran or Syria, but it doesn't mean we shouldn't do away with laws that unfairly punish victimless crimes. Oh and on the topic of overly zealous law enforcement, I'm sick of the overriding mentality that law enforcement is perfect and those who they go after are always at fault. And the same tired arguements that assume that those who have a problem with the police are either a) criminals themselves b) are some kind of anarchists who don't want any law enforcement. Can you say false dichotomy?