Continuity mistake: After Marge says she will marry Homer, at the beginning of the scene, the car is facing the power plant, and at the end, it is facing away from the plant. (00:07:45)
Continuity mistake: Throughout the dinner scene, whenever Homer wants the syrup, it disappears and re-appears next to Lisa.
Continuity mistake: When the mobsters enter Skinner's office, the phone on his desk changes position between shots. Also, the name bar on his desk doesn't read anything on it. (00:13:50)
Continuity mistake: In the beginning, when Bart finds that the dog ate his homework, the poster on Bart's door has disappeared for one shot. (00:01:45)
Continuity mistake: When Moe picks up the "Malaysian Beer" and says they don't serve Duff anymore and how good it is, you then see a shot of Homer talking, then when Moe has put down the beer, it's a Duff .
Tree House of Horror VI - S7-E6
Continuity mistake: In the 'Nightmare on Evergreen Terrace' segment, in Bart's dream you see a shadow of what looks like someone with four knife-fingers. Then when we see who it is, it is Willie holding a rake. But the rake has five tines, not four, so the shadow is wrong. (00:07:00)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: While Bart is in school, Sherri and Terri are making him comfortable. One of the twins vanishes for one shot, and their skin color keeps changing from white to yellow. (00:11:05 - 00:12:15)
Continuity mistake: In the episode which recalls how Homer and Marge got married, Homer writes a note to Marge on a piece of paper entitled 'From The Pen Of Patty' he SCRIBBLES out Patty's name and writes his own, but when Marge reads the note, 'Patty' only has a single straight line through it. The word "HOMER" also changes. (00:14:30)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Millhouse, Bart and Lewis are talking about the fake Santa, Millhouse's eyebrows go from blue to black to blue again. (00:14:15)
Continuity mistake: When Bart and his friends are making copies of the photo of Homer, the banner across the copier says "Copies 5 cents," but when they go to deposit the money it says 10 cents.
Continuity mistake: When Marge and Homer are arguing about Don Quixote, Marge's pillow disappears from under her head. (00:09:50)
Tree House of Horror VI - S7-E6
Continuity mistake: In the 'Nightmare on Evergreen Terrace' segment, in Martin's dream, Willie emerges from the blackboard with a rake which has a wooden handle. When the shot changes the rake handle has changed to being metal. (00:08:25)
Continuity mistake: Just after Bart has played the guitar in the street, he picks up two books. Before Bart picks them up they are green but they instantly turn blue when he does pick them up. Then when he gets on the bus the books have disappeared completely. (00:10:10)
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Genesis Tub', Principal Skinner takes the lid off of the tub, and puts it on the table. In the next shot it's gone. (00:17:55)
Continuity mistake: When Homer, Lenny and Carl are in the cafeteria, and Homer is drinking beer, his chair changes from being blue, to red, then back to blue again, between different shots. (00:06:45 - 00:07:15)
Continuity mistake: At the beginning, when there is an overhead shot of the Simpsons' lawn, the broken lawn mower has disappeared. (00:01:20)
Continuity mistake: While Homer is sleeping, the fire burns off the hair on his head. But when he wakes up and jumps up off the couch, his hair is back again. (00:17:00)
Realty Bites - S9-E9
Continuity mistake: When Marge finds out the Mr Hutz does real estate, the 'For Sale' sign changes from black to red and then back again.
Skinner's Sense of Snow - S12-E8
Continuity mistake: When the hamster Nibbles has rolled back to Skinner, it takes the lid of the ball off, and the lid lands on the ground. When the hamster is rolling away from Skinner it doesn't put the lid back on, it just leaves it on the ground, but in the next shot the lid is suddenly gone.
Tree House of Horror XII - S13-E1
Continuity mistake: At the end of 'Wiz Kids', when Lord Montymort is defeated, he falls to the floor, breaking all the floorboards. Then when Lisa takes off the headset, all the floor is intact. In the next shot, the floorboards are all broken again. (00:20:05)
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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