Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Lisa meets Clara, there is a close up of her necklace. The necklace is never there in any of the other shots that we see her. Her ring, as also seen in the close-up isn't visible either.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Homer is playing the song on the piano, one of the photo frames on the top of it keeps changing from square to oval.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: Carla's "Carla" ring is only on her finger in the closeup.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Luke jumps off of the horse to save the rattlesnake egg, the horse changes from being beside Luke to beside Lisa between shots.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Lisa goes to save Clara, she's wearing the same dress she took to the dance, but after Clara walks safely back to land, Lisa is wearing another outfit entirely, then changes back to her previous outfit in the very next shot, then back to her unknown outfit seconds later.
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