Brother's Little Helper - S11-E2
Continuity mistake: When Homer and Marge are in the research lab, the scientist pulls off a white cloth which is covering the hamster tank and places a tube next to it, but in the next shot it's gone. (00:04:55)
Brother's Little Helper - S11-E2
Audio problem: Homer's mouth is out of sync when he's naming celebrities who use drugs.
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