Continuity mistake: In "Krusty Gets Busted", Krusty's natural skin colour is established as yellow. In "Brush With Greatness" we see him wiping off the clown makeup to reveal that he has yellow skin. But in "Homer's Triple Bypass", he comes to visit Homer, with his white clown face, and tells him that "this isn't make-up". Other episodes after that also show that his skin is white.
Continuity mistake: When the burglar points the gun at Apu and says "Hand over all your money in a paper bag" Apu immediately replies "Yes, yes, I will". But when Bart sees this incident on TV later, the time between the burglar demanding the money and Apu replying "Yes, yes" is much longer.
Continuity mistake: After Sideshow Bob finishes reading his book and puts it on the table, the pages of the book change from yellow to red between shots.
Continuity mistake: When the store is being robbed, Homer throws his bag to the side and it lands face down near the stand of chips Homer jumps into. But when they are watching the video of this incident later, the bag is standing upright, far away from the spot it previously was at.
Continuity mistake: When the robbery happens, Homer steps on the robber's feet, and we can tell he has large shoes. When they show video of the robbery on the news, the robber has regular shoes. During the hearing, they watch the video again. His shoes are back to long again.
Some Enchanted Evening - S1-E13
Continuity mistake: Bart is shown sitting tied up on the couch and Ms. Botz walks in carrying a tied-up Lisa in her arms before dumping her on the sofa alongside Bart. You can see that the rope Ms. Botz has used to bind Lisa is wound right around her body from the neck right down to her ankles. A few shots later when Maggie comes down and frees her, the rope tying Lisa's legs together at the knees has disappeared.
Some Enchanted Evening - S1-E13
Continuity mistake: When Bart and Lisa ask Marge for food while she's waiting for Homer the time on the clock keeps going back and forth.
Some Enchanted Evening - S1-E13
Continuity mistake: When Ms Botz is leading Bart, Lisa and Maggie to the living room, the video she is carrying in her hand is brown. In the next shot, it is now blue, and when she is talking to Bart, it is brown again.
Some Enchanted Evening - S1-E13
Continuity mistake: When Marge and Homer leave for dinner, there is a lipstick mark on the back of the door. The lipstick mark is from the scrapped pilot version ("the Butterfield Incident") in which Homer slams the door on Marge as she tries to kiss him. Some of the animation cells were re-used for the version that ultimately aired on Fox.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer gives Ms Botz her money when she is in her car, she takes it but in the next shot the money is nowhere to be seen.
Some Enchanted Evening - S1-E13
Continuity mistake: When Ms Botz puts Bart and Lisa on the settee after tying them up, the telephone next to the settee is orange, but in the next shot it is now blue, and when Ms Botz goes to switch on the television, the telephone is orange again.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer pours Marge some champagne in the restaurant, you can see there is nothing by the side of Marge's plate. In the next shot, a knife suddenly appears, and in the shot after that, it is gone again.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer and Marge leave the house for the evening, there is initially nothing by the doormat when they leave, but in the next shot two pink cases suddenly appear.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer is putting the shaving foam on his face in the bathroom, he initially puts the can on the left hand side of the shelf, but in the next shot it is near the mirror.
Some Enchanted Evening - S1-E13
Continuity mistake: Before Homer is about to enter the house, the handle is on the left hand side of the door, but a few seconds later the handle is now on the right, and when Marge opens the door, it is back on the left again.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer is speaking to a customer at Moe's Tavern, the customer has a bowl of peanuts in front of him, but in the next shot the bowl disappears.
Some Enchanted Evening - S1-E13
Continuity mistake: When Marge is speaking to Dr. Monroe on the telephone, the doughnuts in the box next to him change between shots.
Some Enchanted Evening - S1-E13
Continuity mistake: When we see a full view of the kitchen after Homer, Bart and Lisa have left, you can see there is a toaster on the sideboard behind Marge, but in the next shot there is now a radio behind her.
Some Enchanted Evening - S1-E13
Continuity mistake: When Homer is eating his breakfast at the start of the episode, there is some green food with his bacon and egg. But when the doughnut lands on his plate there is no green food, and when he is eating the doughnut, the green food is back again.
Some Enchanted Evening - S1-E13
Continuity mistake: When Bart is eating his breakfast at the start of the episode, there is a knife under his arm. The knife disappears in the next shot, and in the shot after that, it is back again.
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