My gripe with anime is from an artistic PoV.
I dislike that almost all vital and important characters in anime are beautiful.
Part of it has to do that a lot of anime is made for the young Japanese male demographic, so the fact that almost all protagonists seem to be jaded and androgynous adolescents doesn't entirely surprise me. But I hate that none of the character designs seem to have any of the real defects or biological flaws that normal,every day people have. No one in anime has jowls, none of them have acne, none of them are freakishly tall or short, none of them are freakishly thin or fat, none of them have snaggle-tooth, none of them have lines in their faces, none of them have strange face proportions that make them unattractive. I'm not seriously expecting to see a change in which the characters are truly fugly, that would be really stupid; but I'm annoyed by the fact that all of them are picturesque and personify the ideal human form. It's like how all western comic book superheroes before the mid 1970s were all white and upper-middle class with mid-western conservative US values. It's not so much that they need to be ugly, I'm just put off by how they are all perfect and that the writers/producers/whoever seem to expect people to somehow identify with them when they start to wangst about minor childhood trauma and dad-issues that made the dark and jaded anti-hero protagonist so darn jaded.
It's a gross generalization, I know, but it occurs often enough that I can say it and I can reasonably assume that you all know what I'm talking about.
Also: the stupid fucking eyes. I'm aware that it's used as a form of wordless expression, but it annoys me and somewhat creeps me out when anime characters do that weird eye-thing they do when they're distressed, awed, or speechlessly-afraid; you know, where their entire eyes bulge and shake dramatically. Yeah - the human eye cannot do that, either they are mutants or they have intense periodic cataracts that plague them at specific plot-important intervals. It's not dramatic: just stupid.
Over-sized weapons: Yeah, it occurs in western stuff too and it still comes across as the said characters/writers/whoever overcompensating for erectile dysfunction and feelings of inadequacy over here too. The Japanese just seemed to make it popular; is that a cultural thing, or some kind of rite of initiation among the artists that has spiraled out of control over time?
I also have a beef with how all anime seems to be built around similar plot points, but I actually understand that and have no questions about it.