I'm not sure what you mean by "derivative work", but I once wrote a scathing four-paragraph review of some fool's Silver/Reader fic on deviantART because she explained literally nothing about where the hell this was taking place, messed up Silver's character, murdered the English language, and called Lyra a whore. (Don't bother looking for it, it's not worth PPCing and the so-called "author" hid my rant anyway.) So there's that.

I also hate when people fail to do the research.

My biggest peeve is fics aggressively shipping pairs that aren't established in canon. (Especially if it means breaking up or ignoring canon romances.)

Also, fics that contradict my personal interpretation of anything that's not been clearly established in canon. (Mostly because they usually tend to go for the most literal interpretations, while I like to think I go for the most interesting and unusual ones.)

Apart from that, just all the usual stuff like Mary Sues, squick, etc.

We know there's at least the Salem Witches' Institute and I'm sure there are others in America. But not only that, but they are almost always taken on a shopping trip in Diagon Alley, even though quite a few of their materials could probably be obtained in the American equivalent, and then they proceed to integrate themselves with the 'Golden Trio' or the Marauders and bleh.

Of course, since those creatures are almost always Sues, I'm okay with that. It means I'll never run out of missions. }:-)