Asian stuff in general often makes no sense to me, unless it tries to be fairly realistic. I think there's a lot of things that make sense to them for cultural reasons that just leave me thinking "what? That doesn't explain anything!" so when we get to the part of the plot that explains what's going on, nothing falls into place. For a reversed example of what I mean: suppose you came from a culture with no concept of ghosts or spirits and you watched a horror film about them for the first time, and spent the whole thing wondering what the bloody hell all these semi-transparent people were doing and why. Watching their horror/fantasy/etc. stories often feels like that for me. Not specific to anime exactly, but I rarely watch live action films from Asian countries so it comes up more in anime.
Bad subtitles or dubbing is definitely annoying as well, depending which there is. I think Trigun was the only dubbed show I ever thought was decent (although I did see a Russian dub of an English live-action film once, and it was surprisingly believable - except that I'd seen the English version before. I've always absolutely despised dubs on live action before, but I had nothing else to do so I sat through it and wasn't completely repulsed).
Also, when action scenes feel less like something coherent that's happening and more like an attempt at inducing seizures. I don't mind so much when things just happen quickly, like following a battle in Macross, but just going from one nonsensical blast of colour to the next with a few shots of someone shouting or growling in between is just annoying.
This is similar to the first thing but I don't think it shares that excuse: things that just plain make no sense. If someone is supposed to have superpowers or something, fine, I get that they do unnatural things. If they don't, I'd rather they stay that way. The same goes for objects. I remember one particular scene in Wolfs Rain in the last few episodes where a car they've left near a ledge falls off a cliff when part of the ledge breaks away. Then later on they're driving this same car which they've got back up the cliff... and it's actually become shorter in the impact (length-wise, not height). Like, significantly. And apparently they just picked it up, dusted it off and went on their merry way. Hilarious as it was, it didn't really fit with the seriousness of that part of the story at all. I have to wonder if the person who came up with that had ever even seen a car before.
