Hmm... there aren't too many things I outright dislike in characters, even though I could be picky when creating/buying designs for myself. I enjoy seeing all sorts of characters, generally, especially when the artists take risks with their designs. I also don't have any problem with self-harm scars, and I welcome characters that have touchy/sensitive aspects to their design (Hope I worded that okay ^^). I've never had a strong negative response to a design; if anything, I get curious.
Rant over... sorry. I think the only thing that I personally don't really like are really cutesy designs. But even those could be wonderful.