I wouldn't call it a pet peeve, but two things that bothered me were Ambipom and Gliscor's leavings.
Ambipom loved Contests and nothing but Contests, which was why Ash traded her to Dawn. She was perfect Pokémon for Dawn. But one day writers decided they want Ambipom go and made her interested in ping pong all of a sudden. Talk about out of character.
Gliscor's leaving wasn't totally out of character, but what bothers me is more what followed after with Gible. Leaving one fully evolved Pokémon for Pokémon who only served as comic relief is so wrong I can't grasp it even these days. The only thing that made it not the worst thing writers did (that title goes to Ambipom's leaving, IMO), was the fact Gliscor retuned for the League.