Continuity mistake: When Marge and Homer are at the Springfield formal ball at the Country Club, about half way through the ball, there is a woman with her back to the camera as she is talking to Marge and Homer. Homer is on Marge's left side. In the next shot when Marge's back is to the camera and you can see Marge still talking to the woman, Homer is no longer on Marge's left side, he is gone.
The Bart Wants What It Wants - S13-E11
Continuity mistake: When Bart is in the ice cream parlor breaking up with Greta, the waiter tells him "We get that a lot around here" and point over to Chief Wiggum and Lou sitting behind and to the left of Bart. Bart turns his head all the way to the side to see them. The focus then goes to Chief Wiggum and Lou, but when their part is done and the "camera" goes back to Bart and Greta, the policemen are sitting behind and to the right of Greta, so that Bart would not have had to turn his head to see them.
Continuity mistake: During the scene where Grandpa is getting married to Amber, his reading glasses appear from nowhere.
Continuity mistake: When Marge and Homer are put in stocks, Marge initially has lipstick on, but in subsequent courtroom scenes it has disappeared.
Continuity mistake: The stocks that are put on Marge and Homer are fitted so that their head and hands are secured and cannot be removed. Whilst in Flanders garage and Homer is using the rotary saw to remove Marge's stock, Homer's stock is still secured on him but his arms and shoulders are through the stocks.
Continuity mistake: When Homer is sleeping on Bart's school floor, Bart puts his shoe in Homer's mouth. Later, when Homer is screaming about "Cobras," the shoe has been coloured black, rather than the usual blue.
Tree House of Horror XII - S13-E1
Continuity mistake: In 'Wiz Kids,' we see Ralph tied up in Lord Montymort's lair. Between a wide shot and closeup, when he says "Dying tickles," his cloak goes from undone to done up. (00:17:05)
Tree House of Horror XII - S13-E1
Continuity mistake: In the end title sequence, the frogman thing vomits and leaves a stain on the parking lot. When Pierce Brosnan drives away in his car, there is no stain. (00:21:05)
Continuity mistake: When Homer is being hypnotised, in some shots there are plates on the Simpsons table, in others there are not.
Continuity mistake: When Homer is having the thanksgiving dinner at Moe's, he isn't wearing a tie, but between shots he suddenly gains a tie. (00:20:35)
Hunka Hunka Burns in Love - S13-E4
Continuity mistake: In one of the shots after Mr Burns has broken the fortune cookie, the remains of it vanish from the table. There is something else on the table, nearer Smithers, but it and the cookie are very different shapes, so it's very difficult to confuse the two.
Sweets and Sour Marge - S13-E8
Continuity mistake: When Lou throws a small chocolate statue in the fire, his skin is yellow when it is usually brown.
Hunka Hunka Burns in Love - S13-E4
Continuity mistake: When they are sitting down in Stu's Disco, there is a little glass next to Mr Burns' glass which vanishes in later shots.
Continuity mistake: At the thanksgiving dinner, Lisa tears one of the legs off of the tofu turkey, but in a later shot the leg is back on the turkey. (00:20:20)
Papa's Got a Brand New Badge - S13-E22
Continuity mistake: When Homer goes to the cupboard, there are no wires to the right of it. However, when Homer plugs in the singing Santa, there are lots of wires trailing to the right. (00:02:40)
Tree House of Horror XII - S13-E1
Continuity mistake: At the end of 'Hex and the City,' there is a shot of the wedding cake, then it pans across the people at the wedding, and you can see Homer with his white shirt on. But then when it goes to a closeup, he suddenly has a blue suit and tie on. (00:06:45 - 00:07:20)
Continuity mistake: At the end of the episode, Homer puts a skull in a box on the coffee table. When Moe arrives to explain his theory, first the box disappears from the coffee table, then the entire table vanishes.
Sweets and Sour Marge - S13-E8
Continuity mistake: When Homer falls off the human pyramid, he grabs onto someones rear end to stop himself from falling. In the next shot, he is suddenly holding a foot.
Continuity mistake: When the family are returning from the picnic, they pull into the drive and Homer has a seatbelt on in some shots, and in others he isn't wearing it. You can't even see it attached to the side of the car sometimes.
Continuity mistake: When Homer first finds the corpse, there is no belt on the trousers it is wearing. But in the shot where Homer starts to scream, there is a belt on the trousers.
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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