Continuity mistake: When Homer is in the hospital, Bart is wearing completely blue shoes. However, when the doctor lays Homer down, Bart's shoes change and have white edges and a white dot. (00:05:40 - 00:06:10)
We're On the Road to D'ohwhere - S17-E11
Continuity mistake: When Lisa tells Marge that Flanders has only bought his own, and as the zoom pulls back to focus on Flanders, Lisa's mouth abruptly opens in one frame and then shuts very abruptly in the next.
Continuity mistake: When Mr. Bergstrom and Homer are eating together, Mr. Bergstrom's left hand is up and holding a fork, but the next shot shows his left hand resting on the table.
Continuity mistake: The long shot of Homer and Mr. Bergstrom eating lunch together at the childrarium shows Mr. Bergstrom's left hand resting on the table, but the next close-up shot of the duo shows Mr. Bergstrom's left hand up, holding a fork.
Continuity mistake: As Homer speaks with Apu before the robbery, Homer has a fudgesickle in his left hand, but when he turns from Apu to leave, the fudgesickle disappears.
Continuity mistake: When Homer tells Lisa he needs "daughter's picks" while he's watching the playoffs, Lisa tucks the pencil behind her ear with its point facing her back, but in the next shot the pencil is tucked the opposite way with its point facing her front.
Continuity mistake: After the Simpsons are selected for the 1895 reality show, they're shown the video confessional room, with the only tech in the house. When Marge is in this room confessing about her blue hair, the doorknob is on the right, but when Bart is inside confessing that he's miserable, the doorknob is on the left side of the door.
Continuity mistake: When Homer brings his family to Lenny's apartment, as Lenny shuts his front door, its doorknob is on the right, but when Homer and his family depart Lenny's crazy apartment, now that front door opens the opposite way, with its doorknob on the left.
Continuity mistake: When Marge opens the dishwasher and tells Lisa to reattach the toilet seat, there's a red dish rack on the counter over the dishwasher, but in the previous and following shots there's a filled casserole dish over the dishwasher, not a dish drying rack.
Continuity mistake: When Mr. Burns realises just how much Grayson is adored by fans, Warburton Parker has multiple bracelets on his right wrist, but in the next shot as Parker tells Burns about the media-driven world, his bracelets have vanished; then after Smithers opens the floor's trapdoor, Parker's bracelets reappear as he falls through the trapdoor.
Continuity mistake: During the episode, Grayson Mathers wears a watch on his wrist that inexplicably vanishes and reappears a few times. First, when Marge is in the school infirmary with Grayson, as he says, "I called Peyton Manning a chicken-fried Frankenstein." Second, when Grayson and Bart tussle after family dinner, and Marge tells them to behave. Third, when Mr. Burns shows up at Grayson's birthday party.
Continuity mistake: This is a mistake for the introduction from seasons 2-20 (1991-2009). When Homer screams, he turns round. You see this in a wide shot. There are no boxes to the right of the door in the garage. However, two just appear out of thin air when he runs through the garage. (00:01:50)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: Lewis changes from black to yellow when Milhouse dares Bart to pull Santa's beard off. (00:14:10)
Continuity mistake: When Homer's Vegas wife shows him the video in front of Marge, it shows Homer kissing Ned. This didn't happen when she showed it in the Vegas episode.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: When you see a shot of the church from outside in the scene where the bee sharps sing there, look closely at the sign. It says 'Also: The Bee Sharps', only they don't name themselves that until later on in that episode.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: While having breakfast, all of the Simpsons' glasses of orange juice keep disappearing and reappearing throughout the scene. (00:05:35)
Continuity mistake: When Bart leaves the school, you can see that his skateboard is green and perfectly flat. But when he is skating through the crowd and past the people at the bus stop, the skateboard has an orange stripe down the middle and is raised at the rear.
Continuity mistake: Ms. Krabapple takes the cellular devices from the children in her class and puts them in a Laramie Cigarette box. She dumps the box into a desk drawer filled with frogs. A few seconds later there is a shot of the class from her point of view with all of their cellular devices on their desks. (00:03:00 - 00:08:15)
The Girl Who Slept Too Little - S17-E2
Continuity mistake: At the end of the episode where Homer is on the field talking to Buck the baseball player, the stadium is crowded. When Homer and Marge are leaving in their baseball golf car one second later, the stadium is empty. (00:20:40)
The Bonfire Of The Manatees - S17-E1
Continuity mistake: When Marge is in the car upset at Homer, the door to their house changes from open to closed then open again between shots.
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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