OK, well, personally, what annoys me is when people try to write fanfics without actually understanding the source material, and make no effort to rectify this. I've seen some really terrible characterisation and plot holes come from that before.
Also, I don't like it when people kill off characters for no reason, or just to be "edgy", particularly if it's someone I like (which mainly means Sakura...). I understand character death is sometimes needed in a story, but just doing it to make the ending look a little less perfect or because you just don't like them is really annoying. Particularly if it's then glossed-over and everyone but that character is perfectly happy.