Continuity mistake: Patty and Skinner go to see 'Space Mutants IV: The Land Down Under'. In a season one episode, 'The Telltale Head', a sign on the Springfield Aztec movie theater reads 'Space Mutants IV: The Trilogy Continues'.
Home Away From Homer - S16-E20
Continuity mistake: We see Coach cutting down trees in Flanders' former driveway. However there had never been any trees in Flanders' driveway.
Continuity mistake: When Red has finished the steak, he lies back and is the same position for Homer's small speech. However, as soon as Homer starts to say 'Wait, you're not breathing,' Red blinks when he is meant to be dead.
Continuity mistake: When Homer and Marge are in bed Marge moves up and we can see she isn't wearing anything, but in the close up you can see that she is wearing her pyjamas - note the thing around her neck, then it's back to nothing.
Continuity mistake: After the slinky leaves Moe's hands, and goes out of Maggie's room, we see that Maggie's toy phone is right next to the door way, then when the camera goes towards Moe, and Maggie, then we see the toy phone next to Moe and Maggie.
The Mook, the Chef, the Wife, and Her Homer - S18-E1
Continuity mistake: When Bart and Fat Tony's accomplices are going to meet Krusty, Krusty's nose can briefly be seen as white when it should be red.
Cape Feare - S5-E2
Continuity mistake: When Bob has finished singing the score of the H.M.S. Pinafore, an English flag comes down. But when he draws his sword to kill Bart, the flag is gone. Where could it have gone?
Continuity mistake: When Barney becomes his old self again at the training center, he gets on a jetpack while holding a bottle. In the next shot while he is in the air, the bottle is gone.
Continuity mistake: When the school bus drops off Bart and Milhouse at the Simpson house, Bart puts his backpack on frontwards and starts krumping. When he walks through The Front door, he is still wearing his backpack on his front. It then cuts to inside the house, and we still see him coming through the door, but the backpack is gone.
Continuity mistake: When the men from Festival Cruise Lines arrive at the Simpson house, they park in the left-hand lane (closest to the house) with the car facing oncoming traffic, seen both when they first pull up and, more, in the background while informing Milhouse about his parents. But in the overhead shot of the house, the car is parked the other way around, following the direction of traffic.
Treehouse of Horror XXI - S22-E4
Continuity mistake: In the second segment, after Roger has told them about what happened to him, a radio appears out of thin air.
Treehouse of Horror XXI - S22-E4
Continuity mistake: In the second segment, as Roger is telling them about what happened to him, as he finishes the story of Marge and Homer saving him, in his recount Marge is wearing a shirt and bikini bottoms (the shirt is covering the bikini bra). But when they saved her, she was just wearing a bikini.
Continuity mistake: After John shows up in his car to take the Simpson family for a drive, Marge has her purse strap hanging off her left shoulder when she asks Homer to at least say hello to John. In the next shot, as she tells Homer that he liked John that morning, note Marge's purse strap is missing from her shoulder, but the purse is still there just hanging in midair under her arm. The strap reappears in its proper place in the next shot. (00:07:50)
The Itchy & Scratchy & Poochie Show - S8-E14
Continuity mistake: During the last taping of Homer's Poochie character, June Bellamy is standing beside Homer, and she's wearing a watch on her left wrist, but her watch vanishes in some shots. (00:19:40)
Continuity mistake: After Brodka lets Bart go with a warning the boy rides his bicycle home, and in the closeup the handlebar's single brake lever is at Bart's right hand, but in the next wide shot the brake lever is at his left hand. In the closeup there's also a bar at the center of the handlebar, but it's gone in the wide shot. (00:09:05)
Continuity mistake: When Brodka brings Bart to the security office and plays the shoplifters video tape, Troy McClure's trench coat buttons are on his right side (viewer's left), but when Brodka turns off the video the buttons are on Troy's left side, between shots. (00:07:30)
Continuity mistake: At bedtime, while we hear Marge singing to Lisa in her bedroom Bart is lying in his bed, and on Bart's nightstand beside the door there's a framed photo of Krusty and an alarm clock, but in the next closeup the photo has vanished and instead there's a Krusty telephone. (00:15:55)
Continuity mistake: While Homer and Barney are smoking in the boys bathroom, when Principal Dondelinger walks in on them the "boys" sign on the exterior side of the door disappears in the closeup, but the sign reappears as Dondelinger exits. The door push plates on both sides of the swing door also vanish/reappear during the scene. (00:04:35)
Brother From the Same Planet - S4-E14
Continuity mistake: After Pepi and Tom walk off into the sunset together it cuts to Bart handing Homer another beer, and the picture behind the couch has brown sails over the boat, but next shot it's colored properly with white sails. (00:21:30)
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.
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