Just putting in my .02...
Hated Anime Elements
face faults-this is probably up there near number one on most hated anime elements list and it's common on anime shows on network TV. Naruto, Bleach, Pokemon, many others that get waay too much airtime here use it to the point of nausea.
Face faults aren't a dealbreaeker for me, since they're normally only used in a sort of over-the-top attempt at humor, which ABSOLUTELY looses something in translation. They're used a lot in younger-targeted anime, because over-the-top emotion is not only funny for kids, it's also simple and identifiable, very elemental. Unfortunately, humor is something that not even an elite bilingual translator can effectively convey very well, so it often comes off as flat and spastic.
BLEACH evokes a lot of over-the-top humor from its supporting cast and its premises, and that doesn't usually translate very well.
chibi animation-interrupting the show so that characaturized(sp?) versions of the characters can act out ridiculous emoticon-like sketches is annoying as hell and far too common in much of what I've seen on networks.
You'll get no disagreement for me, except that I've never seen chibified characters on the networks.
posing-dragonball I'm looking at you! Why do all the characters have a posing match before they fight and why does most of it have to happen on the backdrop of a featureless blue screen? Why can't they just show the fight?
This, I'm actually going to slightly disagree with, because it's definitely NOT just an anime thing. You know that image of Superman atop the logo of the Daily Planet with his cape stretched out behind him? That image of Batman lurking in the high shadows of Gotham? Posing! It comes right out of comic books, and it's surely something I try to do in my evocative D&D descriptions. An acrobatic dance out of the path of a fireball, or a triumphant deciding slash with your sword...that moment of awe-inspiring coolness.
naming moves/weapons/anything-dragonball again, but many others inuyasha included. Why is it that the characters all have to scream out the ridiculous names of their fighting moves? Why can't they just FIGHT, instead of spending half the scene screaming out some awful transliterated title?
Again, I think this is absolutely relevant for D&D. Wizards are always screaming out some awful gibberish before they unleash the giant ball of fire.

It's all about the verbal chant of arcane energy! It's also relevant to martial arts...this isn't just a punch, this is the legendary Dragon Punch, handed down for generations of fighters from the Whatever School of Awesome Arts. Screaming the name lets your enemies know that it's not just you they face -- it's the collected wisdom of all those who have trained you.
Admittedly, I can't see anyone in a fight actually doing that...but the identification of classic moves is a staple even in European fencing styles, so moves having names (and people being able to identify them) makes sense to me.
angst overload-Here I'm definitely pointing at half the anime on network TV in my area including Naruto. Specifically the heroes who aren't yet fifteen and act like it, why all the involved angst over mundane things. Why must the heroes all become completely useless whenever a female becomes involved and are completely unable to just talk with the female in question?
It's called "building tension."

Yeah, it's overplayed and over-developed a lot...InuYasha is perhaps the worst offender where the love triangle between Girl-Half-Demon-Undead Ex-Girlfriend has been going on for an absurd length of time.
But this isn't unique to anime, either. How long did the Ross and Rachel drama on Friends go on, after all?
incompetent/stupid hero-Okay Naruto is the king of this one as far as I've seen on network TV here. I mean the hero is dense as a rock, and completely incompetent right up until the moment plot requires he win, at which point he suddenly becomes much more powerful and trounces the opponent at the last minute. Then immediately goes back to being a moron immediately after.
The "idiot savant" is a solid archetype, though. You've got the role of the Jester or Fool, the lucky moron, the normal guy with the incredible will....you could even say Frodo and Samwise fit this archetype: they're piddly little things who rise to the challenge when it's presented. Sam goes back and lives a comfortable hobbit-life in the Shire when he's done, and he never stops talking about what he's cooking. Maybe Merry and Pippin fit it even better.
That's also an aspect of the sluggish character growth in a lot of Anime, though: Naruto *will* become competent and powerful, it'll just take seven years of animation to get there (more, if it's a successful series).
