Here are a few examples to start you off.
Often in Ranma (and perhaps other shows, but I can't name any offhand), when a character hits another character, or a chracter hits a tree or whatever, there will be some sort of yellow-on-black geometric "impact" graphics. But often a frame of unrelated art will be thrown in for fun. Here's part of a frame from when a character gets hit in one episode. Several frames on either side are merely simple abstract "collision" graphics. (I cleaned it up a little. The quality and encoding of the show aren't the best)

In the first Ranma movie, when Monron attacks, they throw this in for a few frames. (It's onscreen longer than I remember it being, actually. Of course, the scenes on either side are longer than the relative blip in the middle)

I wouldn't have noticed this error if I hadn't been staring at the scene while working on Doomrider. His hands are drawn backwards!

haha
And here is a blatant error in the final episode of Fushigi Yuugi. It only appears for two frames, however, when the screen is flashing/inverting because of a fight between Nakago and Tamahome.

Finally, Rozard posted an interesting example of some flawed Bleach DVD footage on LiveJournal a year ago.