Characterisation is what makes me squeal most in the fics I love, but even so I can't think of anything duller than showing no other sides to a character to those already seen in the books. I *want* to see the characters when they aren't around Harry, or aren't in public. I *want* to see what they are like at home, with their family, or whatever, and since we don't know it is always going to be fanon. I can accept a wide range of characterisation, and as I love future fics perhaps more than some. It's the exploration I like to see, whether it incorporates stuff from the films or other plausible scenarios - just (as you say) don't give me completely implausible and unrecognisable characters.