I've got a few beefs.
1- Overcomplicated plots that require a guide to understand.
Inuyasha and the Dragonball franchise are a few that like to do this. The latter I could excuse because I used to watch every episode on Toonami, or at least try to. However, it still had the problem of "if you miss a few episodes you miss the whole series." Animes like Cowboy Bebop don't do this a lot. Sure they have a few running plot points, but the show at it's core is about a group of bounty hunters who suck and can't get a break. Comedy animes like Cromartie High School are also good because they just give you a cast of characters and then leave what happens to the writers. The over complicated ones are complicated because they are TOO BLOODY LONG. Since the show does well, they have to keep it going with one stupid plot to another stupid plot over and over, while STILL not completeing the plot they had in mind in the first place.
2- Stupid gimmicks.
Death Note had a nice gimmick: the lead character/villian had a notebook that can kill people. The anime was balanced out with a excellent, suspenseful plot. That is a gimmick done right. Then you got stuff like Code Geass, which I haven't really got into. It's just another anime with robots and tits and one of the gimmicks is that he has some kind of GoldenEye thing in his skull like the grown up Enzo from Reboot.
3- Unmoderated use of breasts
Everyone likes breasts. But goddamn I see too many that use it as a selling point; trying to cover up humongous flaws with a pair of H cups. Also, like Ak-Jay menioned, some are underaged and not explained immediatly. The Izuna DS series, not an anime but close enough, is a big offender of this. Back to the main topic, breasts need to be used in moderation. I don't want to watch an anime with my cock out unless it is an advertised hentai. Some also like to take it a step forward by giving everyone large breasts and unnatural jiggling to make up for paper cutout personalities; Divergence Eve and Goddannar are animes with basic looking plots that use tits to make up for them, which I why I refuse to watch them. Then you got shit like Eiken. Goddamn Eiken.
4- Too Japanese
South Park was made for a western audience. Anyone who has watched FLCL with the commentary on (or have just watched the style parody in episode 5) would know that South Park didn't do well in Japanese markets because the jokes didn't make sense to them. It's the same thing over here, but we just eat the shit up like a crate full of Pocky. Some animes are made with overly Japanese themes and humor because they were made with the intention of humoring the locals. Over here, they just leave audiences in the dark; at least the ones that don't go onto forums and try to speak Japanese and all that shit. My example for his one? BoBoBo. This one is a tragety because it's absurd, fast paced humor was something that I would've liked. Eventually, I just grew tired of it. The final straw though came from a chaged translation that ruined everything for me, which i'll get to in a bit. Meanwhile, FLCL changed the Japanese references to western ones, which may have piss off some weeaboos, but not me; I can understand why they did it. What BoBoBo did was, in one episode, said that Jelly Jiggler was "some kind of ninja" when he was obviously trying to be a Shinto priest. (there were shost flying about) By now people were fam ilar with Inuyasha's Shinto preists since they bring it up every episode, and Jelly Jiggler wasn't even DRESSED like a ninja!
A couple animes that get off the hook with the whole "too Japanese" thing are ones like Cromartie High School and Azumanga Diaoh that keep it to a minimum and would sometimes have 'cultural notes' on the DVDs.
5- Tried and true themes.
I don't watch Mecha animes. I've seen Gundam Wing and I could bring myself to watching Neon Genesis, but the whole fighting robot thing is now just being a hooker for unimaginative writers. There's too many of them! Someone up there also brought up the harem anime, or at least animes with the whole "socially awkward boy lives with a large number of attractive women" gimmick. For me, the jury is still out on the matter. One of my favorite animes growing up was Tenchi Universe which, in retrospect, had characters that were likable and girls who were not over-the-cup breast creatures. But I see where he is coming from; they too are many in number, usually in the hentai genre,(who also like to do the whole "he's not blood related, so let's fuck him" thing) and some are just made to give the fanboys more tits to look at during the obligatory bath scenes. (YES, Tenchi had that too. But once again, the girls were actually more down to Earth and not sentient blow up dolls.) Honorable mentions include anything that involves space travel, Japanese High Schools, and feudal Japan.
But really, these are things that were made for the amusement of Japan exclusively. Some people just want them to be imported over here because they're too lazy to import or just watch YouTube clips. This is shit that Western audiences don't understand, and shows like Excel Saga show that not even the Japanese understand! In conclusion, anime is made for money and japanese television. They've proved to be a respectable form of animation now, which now opens the door for exploitation works that, despite what all the little fan cults want to convince that isn't true, are made for a quick buck or just filler.