Having characters with levels of competence that are vastly different from what they should be, based on what we know of the character. I find this happens a lot with female characters, in one of two forms.
a) a woman who's never had any kind of fight training/experience, suddenly insists on being included in dangerous situations, in order to make an "action girl" scenario happen. I understand wanting to avoid the damsel in distress cliches, but sometimes it's just silly.
b) a woman who's a police officer/military etc, really should be competent, constantly getting kidnapped and needing to be rescued. It's insulting.
I feel like both these are trying to have it both ways, and also often only having 1 woman in a whole series so they have to put every single trait on her. instead of having your rescue plot happen to, say, a kindergarten teacher (and she can be awesome in other, non-combat ways) and the female police officer being the one to beat the bad guys. Or, maybe they are trying to be subversive only these things are now so common as to be predictable...