My kids (DD2 and DS5) are actually not very sensitive when it comes to movies. They've been pretty good with some "scary" movies (e.g. Ghostbusters and Harry Potter). My husband has no filter when it comes to media, so the kids have seen snippets of things that I wouldn't have let them see from his channel surfing, like Walking Dead or Platoon.
The thing I am really going to have to start monitoring, though, is music videos. They both really like pop music, so they'll sometimes ask to watch the video that goes along with the song they like. Those tend to have inappropriate sexual things, which I don't want them to pick up. Already from seeing stuff on tv and Frozen, my tiny daughter has the idea that people should kiss with open mouths.