Love, Springfieldian Style - S19-E12
Continuity mistake: In the third story of the episode, Bart and Nelson throw Martin into the Jukebox despite it never being opened. When he is trapped inside the box the glass is firmly in place as well.
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Factual error: The symbols on the heads of the Teletubbies on stage are wrong. They did use the word 'teletubbies', so they're meant to be the same as the real world. (00:05:40)
Continuity mistake: Near the end when Homer is going into the show, he is not holding his coat. Then it appears in his hands and gets stolen. In the very next scene, he then wears his coat again. (00:19:40)
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