I know it's a budget thing, but I hate when characters are seen wearing the same clothes all the time. And I don't mean school uniforms, because that makes sense that they'd be in it often. But their own clothes - no one wears one set of clothes. xD
Also, how everything seems to be set in Golden Hour. D:
Anime is getting better at that, I do know some animes where the charters do get a change in clothes.
Well... the art style that most anime is done in is an immediate pet peeve for me. All the bland samefaces just drive me up the wall. I don't know if that counts as an animation pet peeve, but there you go.
Also, how some series animate boobs. Giving boobs a lot of motion is okay if you can do it right, but if you make them flail around like they're full of mice or something it's not sexy anymore. It's just disturbing. If a character's breasts are moving and she's not moving (and it's not being played for comedy), something is seriously wrong.
I hate it when they have ridiculously pointy noses, like in Escaflowne, and I think in Witch Hunter Robin, but not quite as bad. And, like how some other people mentioned, when there are CGed things and anime things on at the same time. And recently I was slightly disturbed by unnecessary boob jiggling, such as was mentioned before, but accompanied with a disturbing sound effect... Not a bouncing one, like you'd think, a sloshing one...
I don't expect the average anime series to be well animated. I expect low frames of animation, for there to be long periods of dialog where the characters don't move at all. I expect the face to not move when they talk. I expect for large action scenes for the background to vanish. I expect still character movements.
I may point these things out when people confuse animation with character design but that's different. These things don't bother me because I realize the average anime does not have a huge budget.
You know what does bother me. The intro having much better animation then the actual series. I know why they do this, it's the intro that draws people in. So it tends to have fluid character animation, fights and character movements much more impressive then the actual series and are just stunning. The idea is to get out intention in the first minute and a half believing that we won't leave if the intro is great. Of course the intro is also a way to get money for the series as they often use licensed music.
Still it really pisses me off in an action anime when there is this great beautifully animated fight in the intro and then the fights in the series itself are choppy, filled with close ups and speed lines used to cut animation costs.