Continuity mistake: After Marge is looking at the matchbox from the Maison Derriere it just disappears when she sits on the sofa.
Continuity mistake: When the remote controlled plane crashes into the roof of the burlesque house, it is seen to hit only the side of the roof, yet when Bart goes to reclaim the plane, it is nested on the top of the roof.
Continuity mistake: At The Town meeting Mayor Quimby's tan disappears in the middle of the scene.
Continuity mistake: When Marge arrives after the song, Flanders and Lovejoy are talking to her, and behind them you can see a crowd of people. The crowd then disappears in one shot, only to reappear a shot later.
Continuity mistake: At the end of the episode when Marge is first seen doing the entertainment, the shot shows (from left to right): Flanders, Skinner, Kirk Van Houten, Kent Brockman, Mayor Quimby, Grandpa, and behind them, Lionel Hutz, Lenny, Homer and Dr Hibbert. In a following shot from behind Marge the guests have changed places. Reverend Lovejoy is on the end, then Flanders, then Skinner, then Mr Burns, then Grandpa. There is a seat next to Grandpa which is blocked by Marge's head. Also Lionel Hutz has moved far back. Where did Burns appear from and where did Kirk, Mayor Quimby, and Kent Brockman all go?
Continuity mistake: After Bart is sent to Maison Derierre, he knocks on the door. Belle answers it and for a couple of frames her arm is naked. Then suddenly her corset appears on her arm.
Continuity mistake: When the angry mob smash all the statues and the fountain before the song, during the song you can see all the statues and the fountain intact.
Continuity mistake: When Marge goes to see Belle at the Maison Derriere she sits down with her.At first there is a white ornament on the small table in front of them but then at the end of the scene it has vanished.
Continuity mistake: During the big song near the end, there is a birds eye view of everybody outside dancing and singing, and Krusty, Chief Wiggum and Skinner are there outside with everyone. But in the very next shot, they all appear out one of the windows, singing a line to the song.
Continuity mistake: When the mob is at the gates of Belle's house, the door bell is first seen on the left hand side of the gates. In the next shot (behind Flanders) it is in the center of the gates.
Continuity mistake: At The Town hall meeting Mayor Quimby's microphone is first seen to be plain grey. In the following shot it has dark lines on it.
Continuity mistake: When Bart climbs on the roof to get the remote control plane, he falls, and smashes into a gargoyle which falls and smashes beneath him. But when he is hanging from the roof, below him the gargoyle is nowhere to be seen.
Continuity mistake: When Helen and Reverend Lovejoy are singing to Belle, in the big song, Principal Skinner and Apu are standing behind them. In the next shot, they've disappeared.
Continuity mistake: When Marge is standing by the bulldozer, someone fires an arrow which is set alight, and it lands on a tree. But in the next shot the tree in which the arrow landed on has vanished.
Continuity mistake: When Homer starts the song at the end of the episode, the doors to the house behind him are open. In the next shot of the house they are closed, then they are open again in the next shot.
Continuity mistake: During Bart's stand-up comedy routine, Dr. Nick is seen wearing his usual white lab coat, but in the very next shot of the audience laughing, he is not wearing a coat.
Continuity mistake: During The Town hall scene, Ruth Powers (the woman with the red bandana) is seen with blondish hair in two shots. All other shots of her during this scene shows her with her usual brown hair.
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.