To me, it'd be the whole "high-school" setting it itself. I'd not mind seeing something that is placed in the world of adults.
I have seen -one- animé that is believable in it's story: You're Under Arrest- a "Body Cop" show about two Tokyo Policewomen.
A good watch, and the only intended fan-service is as much part of the plot-line of the episode as much as it is eye-candy.
And, before I forget... the one-dimensional characters.
The whole "-dere" niche in the animé-world is a result of characters only have one or two personality types (see TVtropes for an explanation of the "-dere" concept), which turns characters either dark emo, or happy-go-lucky idiots.
Of course, these requests would make new material expensive and difficult to produce, but it wouldn't hurt to actually see shows that doesn't take more than four seasons for the characters to become "real" characters (why am I thinking of the long runners (Naruto, One Piece, Avatar, Bleach) in this one?).
There are exceptions to this: I can name a few, but I won't- they don't need to be mentioned or analysed.