My Mother the Carjacker - S15-E2
Continuity mistake: When Homer is looking for a message to stop Grandma Simpson and the jail bus on the electric sign he has Bart with him. Then Bart is not on the bus with Homer and Grandma, but he is back at the end of the episode.
My Mother the Carjacker - S15-E2
Other mistake: In the scene where the prisoners are singing along with Mona, two inmates have the same Identity number.
My Mother the Carjacker - S15-E2
Continuity mistake: At the end of the episode when Homer is looking for another message from his mom to find out if she's really alive, Marge and the kids enter the kitchen, Marge says that it's 2 in the morning. But the clock on the wall shows that it's 9 pm.
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