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)
Million Dollar Maybe - S21-E11
Continuity mistake: When the bulls are stampeding, people who were at the top of the stadium and safe can be seen running in front of the bulls.
Continuity mistake: Just before Apu has a flashback of Helen Lovejoy and Moe interacting in the church, Reverend Lovejoy is in his black shirt and collar. after the flashback he is in his casual pink shirt and blue tie.
Continuity mistake: When Mr. Burns is confronting Homer about his missing slave, Homer's donut is half eaten. During the next scene the donut has a smaller bite taken out of it. (00:14:00)
Continuity mistake: When Scratchy's head gets sucked into the dam pipe, the back of his head goes in first, but when he is shot out, he is facing forward.
Once Upon a Time in Springfield - S21-E10
Continuity mistake: Mr. Burns shows a box of doughnuts coloured pink, brown and light brown. When the guys grab them they're all pink.
American History X-cellent - S21-E17
Continuity mistake: When Homer, Carl and Lenny are drinking at Moe's Tavern, Smithers' bottle in front of them on the table changes position between shots.
American History X-cellent - S21-E17
Continuity mistake: When Smithers walks up the desk in his office, there is a box of items in The Front of his desk. But when he is looking at a portrait of Mr Burns, the box is now on the side of the desk.
American History X-cellent - S21-E17
Continuity mistake: When Marge is speaking to Bart, Homer comes out of the house with a pumpkin and you can see there is nothing on the doorstep. But when Marge goes to the car, a green doormat has suddenly appeared, and when she leaves, it has gone again.
American History X-cellent - S21-E17
Continuity mistake: When the policeman is speaking to Mr Burns about the stolen artwork, the molding on the door behind Mr Burns changes between shots.
American History X-cellent - S21-E17
Continuity mistake: When Homer (dressed in a knight's costume) is about to hit a book with his weapon at Mr Burns' place, there is a wine bottle beside him that disappears in the next shot.
American History X-cellent - S21-E17
Continuity mistake: When Homer is showing Carl and Lenny the large bottle of wine he has found in the wine cellar, you can see there is nothing on the shield on the label, but when see Homer holding the bottle a few seconds later, the shield has now two lines on it.
American History X-cellent - S21-E17
Continuity mistake: When Homer is powdering his face at the make-up table at the Independence Day Picnic, you can see the door to the wine cellar is open, but in the next shot it is closed.
American History X-cellent - S21-E17
Continuity mistake: When Mr Burns is being served ribs at the Independence Day Picnic, there is a knife and fork by the side of his plate. In the next shot, both items have disappeared.
American History X-cellent - S21-E17
Continuity mistake: When Mr Burns is doing is speech at the conference, the stand initially has nothing on it but later on a microphone appears from nowhere.
American History X-cellent - S21-E17
Continuity mistake: When we see Homer in the audience at the conference at the beginning of the episode, he is sitting between a lady with grey hair and a man with black hair. But when we see a wide view of the audience a little later on, he is now sitting between a man with brown hair and a bald-headed man.
Continuity mistake: In Apu's van, one of the octuplets on the left is wearing blue pyjamas while the lullaby is playing, then changes to pink pyjamas after Apu takes the disk out.
Postcards from the Wedge - S21-E14
Continuity mistake: When Lisa is talking to Bart in her room, Lisa's necklace is red rather than white when Bart shouts "End all life on this planet!" (00:08:05)
Continuity mistake: When Carl and Lenny are lowering Homer onto the train window, Lenny's five o'clock shadow is missing.
Rednecks and Broomsticks - S21-E7
Continuity mistake: When the Simpsons are on the highway, Apu's car is seen, and some of the octuplets have yellow skin and blonde 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.
Xofer