Huh, a lot of my hatred came very early in the topic. Two things haven't been mentioned yet though:
Furries- even if the character is interesting, I simply won't watch an anime where humans have tails and animal ears. This annoys me to no end.
The hair- Yes, I know, but come on...
EDIT: I completely forgot this (probably because it's more of a general pet peeve than an anime related one)- bad writing. I don't know if this is due to mistranslation or due to the sheer number of anime out there (meaning that the more there are, the lower percentage of good material).