Continuity mistake: In the scene where Homer is going down the escalator, in the Costington's Centre, after he gets on two men follow him, then a woman, yet when the shot changes, it's a man then a woman then the other man. (00:00:45)
Factual error: The tongue Lisa sleeps on in the museum isn't anatomically correct. It shows the bitter and sweet taste buds as being side by side on the surface of the tongue. In reality, different taste buds are not in specific places on the tongue. I wouldn't normally complain, but this is supposed to be in a museum.
Continuity mistake: Near the start when Marge is putting jam on bread, she spreads it on the last piece but as she puts it on the plate it changes to a blob in the middle.
Continuity mistake: When Homer is driving to Truckasaurus there is a wide shot of the road with two cars on it, but in the next side shot of the road, the road has loads more cars on it. (00:06:30)
Continuity mistake: When Marge is cleaning the dishes on the morning after Bart reveals Lisa as a nerd, Marge is seen in close-up with a white necklace. In next shot of Bart and Lisa, as well as the rest of the scene, Marge has a red necklace.
Sideshow Bob's Last Gleaming - S7-E9
Continuity mistake: When Bart and Lisa first enter the Duff Blimp, Bart doesn't have his back-pack on. However, he is suddenly wearing it after the bomb has gone off.
Continuity mistake: When we see the wide shot of all the houses going along the road, you can see that Moe's door is facing away from the Simpson's house. But in the next shot, Homer jumps in through Moe's door, it's like the tavern did a 180 degree turn.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Homer comes into the kitchen he is holding a pipe in his left hand. But in the next shot you see him holding up the ruined jacket with his left hand, then in the next shot his hand is back in his pocket.
Much Apu About Nothing - S7-E23
Continuity mistake: Homer comes to the Kwik-E-Mart with the new 'American Apu' and sees him reading a magazine. When Apu walks over to Homer, his magazine disappears.
Homer Alone - S3-E15
Continuity mistake: In the scene Marge goes crazy in the car, Homer is let through, and he passes under 'distressed mother' police tape, but in the next shot, the tape has disappeared. (00:06:40)
Tree House of Horror VI - S7-E6
Continuity mistake: When the advertisement of Kent Brockman comes to life he is a thin cut out from a bill board, however the next time you see him he is in the shape of Kent Brockman and no longer thin.
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: When we see The Town at the meeting, Smithers is sitting in front of Selma. In the next shot, though, Smithers is suddenly on stage holding the 'SSCCATAGAPP' sign and Lenny is sitting in front of Selma. (00:08:50)
Radio Bart - S3-E13
Other mistake: When Bart falls down the well because Eddie tripped the rope, why would there be rocks falling down with him? (00:16:00)
Much Apu About Nothing - S7-E23
Continuity mistake: In the early scene where the Simpsons are gathered around the table to eat, you can see that they are eating slices of pie. However, on some of the long shots, the food on their plates changes and looks more like mashed potato and vegetables. Also, in the same scene, in one shot of Lisa, you can see Bart's hand over her plate, but when the angle changes, it is behind her plate.
Alone Again Natura-Diddly - S11-E14
Continuity mistake: Homer's watch disappears when he is getting his car fixed.
Continuity mistake: When Homer sees that Bart and Lisa aren't listening to his story, he looks around the living room while sitting on the couch. He appears beside the window in the next shot. (00:03:30)
Other mistake: When Homer leaves the window, the TV is in a different area of the living room. (00:03:50)
Continuity mistake: In the flashback, at the Aztec Theater, the person in front of Marge and Homer changes. (00:04:40)
Springfield Connection - S6-E23
Continuity mistake: When Marge is shopping, there is a blue baby seat in her trolley. In a following shot of her running with the trolley and it going into the cheese display, the seat has gone.
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