I don't read fanfiction that much mostly because I like to read about obscure characters which never get written about.
Nah it's actually because fanfic scarred me for life. 
I wouldn't say there's anything I particularly hate (apart from maybe going into excruciating detail regarding certain NSFW topics), but here's a few things that put me off:
- Bad formatting and grammar. I don't care if it's the best idea in the world, I can't focus through a block of text especially if you don't know what a comma or full stop/period is.
- As Mouse said, humans in non-human fandoms. Saying that I have read and enjoyed sci-fi LBT fics that involve humans.
- Not tagging your fanfics correctly. If I come across something icky that wasn't tagged, I'm gonna... not like you very much.

- Character bashing. Fine if you don't like a character, but dedicating that much time to hating on them through fanfic is something I'll never understand.
- "
Oh no! Anyway..." moments. I do get irked if something traumatic happens and the characters just shrug it off as an everyday thing. If a character is established as stoic then okay, but if you know the character will be affected and don't show it, then I'm going to struggle with it.
- Mary Sues. Saying that some Mary Sue fics are very entertaining.
- Making characters extremely OOC for no reason.
- Unfinished fics, especially if they're left on a cliffhanger. I understand authors lose interest or have life things going on though. It's why I now won't upload anything until I'm sure it's going to be finished. So far I haven't finished one of my fics, but then they're all pretty long.