The Springfield Files - S8-E10
Continuity mistake: After the scene with the T-shirts, when the alien arives, Marge's "Homer is a dope" shirt disappears and she has her normal dress on.
The Springfield Files - S8-E10
Continuity mistake: At the kitchen table, when Homer talks about getting mocked on his own birthday, they're eating breakfast. But when Marge, Lisa, Bart and Maggie all go to pet Santa's Little Helper, the breakfast has vanished.
The Springfield Files - S8-E10
Continuity mistake: When the 'alien' is seen on the news, it is shown on the film Bart made coming out of the trees, but earlier on, when the alien came out of the woods, Bart is seen not holding the video camera.
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