BAD WRITING
I am extremely picky about what fanfiction I read. I really can't stand poor writing. It goes beyond just grammar and spelling. Someone might be able to create a grammatically correct sentence with all the words spelled right, but it still doesn't make it a GOOD sentence.
If the fanfic doesn't grab me within the first few paragraphs, I don't bother reading onwards, unless someone has recommended it to me and promised that it gets better as it goes or something.
I want to be entertained when I read fanfiction. I want to feel like I'm getting to see more of the characters and the world I love from canon. When the writing is boring or the plot is generic, that isn't entertaining.
I also dislike characters not acting like themselves -
unless it's for a good reason. OOCness drives me crazy, unless the author presents a viable reason for the character to be acting different.
Generally, I prefer reading fanfiction that is written by people who actually write original work in addition to fanfiction. Not that they post original work, but the fact that they write it (especially if they're in some sort of writing group or club) shows that they have the ability to come up with new and interesting ideas. And that bleeds into their fanfiction. Which makes me happy.
Another thing I dislike in fanfiction - sexual stuff being included
when it is obvious the author is only writing so that they can include it. I do not mind "M" rated fics if they're of a pairing I agree with, and is of age, etc, AS LONG AS IT IS
NOT THE FOCUS OF THE STORY. If there is an "M" rated section of a fanfic, it HAS to flow with the story, it CAN'T happen every other page, and it CAN'T be why the author is writing. If they're writing just to have an excuse to think about certain characters getting it on, then chances are the plot of their fanfic isn't going to be well thought out and will be extremely disappointing to read. Sex isn't a "plot". Ugh. When sex is trying to be the plot, that's usually called "porn", people. HOWEVER, "M" rated stuff
can be used to drive a plot or a subplot. If it is done tastefully and not done too often (and it doesn't sound like I'm reading a script to a porno), I will read a fanfic rated "M". But only in certain fandoms. I never read stuff involving or even IMPLYING "M" things for my fandoms that revolve around kids - ie, JN, Avatar, several of my elementary school animes, etc...even if the author has "aged them up".

I just think it's creepy to imagine the children you watch on TV hooking up like that.
Another thing, on a similar note - switching people's canon love interests. In other words, non-canon pairings.
I'm somewhat lax with an author pairing up two characters who didn't have ANY canon pairing, because they're kind of a blank slate where romance in concerned. But I really dislike stories that try to force two characters together that weren't interested in each other in the book/show/movie/etc. Because that is naturally going to be OOC for them. And as I mentioned earlier, I don't like that.
Finally, I don't like fanfics where it is clear the author has absolutely no idea where the story is going. Not that every fanfic needs to have a thorough outline from the beginning, but authors should at least have some sense right from the get go of where they're taking this plot, and what the major events are. That will allow them to drop in clues, and create relevant side plots as they go. Much more enjoyable that way.