Continuity mistake: When we see Lisa eating her dinner, she has a glass of water by her plate. But when we see a full view of the table, the glass has gone.
Continuity mistake: When Adil is speaking to Lisa at dinner at the Simpsons' house, Lisa has a knife and spoon by the side of her dish. In the next shot, both items have disappeared.
Continuity mistake: When Bart is sitting in the bike passenger seat on his way to the Chateau Maison in France, you can see the seat is coloured brown, but when he arrives at the Chateau, the seat is now blue.
Continuity mistake: When Homer is saying goodbye to Bart at the airport, there is a metal fence behind him that changes position between shots.
Continuity mistake: When Principal Skinner is speaking to Marge and Homer, Homer is lying on the settee and you can see there is nothing beside it, but in the next shot his beer can appears from nowhere.
Continuity mistake: When Principal Skinner rings the doorbell of the Simpsons' house, the handle on the door is pink. But when Marge is at the door, the handle is now light blue.
Continuity mistake: When Principal Skinner and his mother are with Bart and his friends after the toilet prank, you can see Bart has Milhouse, Richard and Lewis are beside him. In one shot, Bart is on his own and the other three boys have gone, and in the next shot, they are back again.
Continuity mistake: Bart throws in a microscope in the cupboard of his bedroom when his mother leaves, but in the next shot the microscope is nowhere to be seen.
Continuity mistake: When Marge leaves Bart's room, you can see there is a cap on the mirror on the drawers, but when we see a full view of the room a couple of shots later, the cap has gone.
Continuity mistake: When Bart discovers a pink box by his bed, you can see there is nothing hanging out from the drawer behind him, but in a close-up of Bart in the next shot, a sock suddenly appears.
Continuity mistake: When Homer falls down the stairs, the toy clown lands behind him and a close-up of Homer shows an orange plant pot by the stairs. But when we see a overhead view of Homer lying down, the plant pot is nowhere to be seen.
Continuity mistake: When Marge enters Bart's bedroom, on the wall you can see a picture of a space rocket and on it there is a red cloth. But when we see a close-up of Marge in the next shot, the cloth has gone.
There's No Disgrace Like Home - S1-E4
Revealing mistake: When the Simpsons are eating at the dinner table, Marge's necklace keeps flashing white.
Revealing mistake: When Bart makes a copy of his photo for Lewis, footage of Milhouse inserting a coin into the copy machine is used. You can see Milhouse's pink shirt sleeve instead of Bart's orange shirt sleeve. This same shot is again reused a third time seconds later. (00:09:55)
Continuity mistake: During the theater scene, the man in the back with the moustache and green jacket watching the Space Mutants movie changes from having yellow skin to brown skin after Bart blows a raspberry. (00:09:30)
Revealing mistake: The blonde woman's midriff (from the Space Mutants movie) flashes pink for a frame.
Continuity mistake: When Bart returns home while Lisa is watching Krusty, the door opens without Bart even touching it. (00:22:00)
Revealing mistake: When Barney says "How long will the story take?" after Bart offers to tell the mob his story, the upper half of Barney's face starting from his nose is a darker shade of yellow than his lower half. His shirt also changes colour. (00:01:40)
Revealing mistake: In the beginning, when the angry mob is chasing after Homer and Bart, there are two Dr Marvin Monroes. One of them is behind Mrs Krabappel and the other is next to Grampa Simpson. (00:01:40)
Continuity mistake: At the end when Nelson's goons are holding on to Nelson, they both have brown skin. But in the next shot, one of them goes back to having yellow skin.
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