Continuity mistake: When Bart falls down the stairs, you see him fall down at least 50 stairs in the close up. There are never this many on the full shots of the staircase.
Continuity mistake: When Lisa arrives at Dr. Nick's, amongst the wheelbarrow line is a Professor Frink (and he's not even first in the cue). However, just a few minutes later, when Lisa ends up in the mud pit, we can see Frink amongst the crowd.
Answer: I'm not sure if this is the one you're thinking of, but an episode of "Ray Bradbury Theatre," called "A Sound of Thunder," dealt with a similar matter: a group of hunters travel back in time to hunt dinosaurs, only to find things have changed when they get back because someone stepped on a butterfly.
Xofer