Tree House of Horror XII - S13-E1
Continuity mistake: At the end of 'Hex and the City,' there is a shot of the wedding cake, then it pans across the people at the wedding, and you can see Homer with his white shirt on. But then when it goes to a closeup, he suddenly has a blue suit and tie on. (00:06:45 - 00:07:20)
Skinner's Sense of Snow - S12-E8
Continuity mistake: When the Hamster rolls through the glass of Flanders car it breaks it near the bottom middle of The Front windshield. Later on when Flanders and Homer are taking the kids home you can see the break in the glass has now moved to about halfway up The Front windshield. On of the following shots it moves back to its original position and then moves back to being around the middle of the windshield.
Continuity mistake: The colour of the alien poster in the nerds' room changes from pink to blue.
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: After Maggie makes her wish, the family jumps from being in their seats to beside the window. (00:03:50)
Continuity mistake: At the beginning, when we see the exterior shot of the bus, it is full of kids. In the interior shots, 1) before the twins talk to Bart and Milhouse, every seat is empty, even Sherri and Terri's. 2) when the bus arrives at the school, we AGAIN see a full busload of kids. (00:01:30 - 00:02:25)
Homer Alone - S3-E15
Continuity mistake: In the scene where Maggie rips of the top of her bottle, the milk spills everywhere, including on Marge's face. After this Marge goes really crazy and starts screaming. Right before she does this the milk on her face disappears. (00:04:50)
Continuity mistake: Patty sprays Barney with pepper spray. It disappears from her hand in the next shot. (00:18:55)
Lisa's Pony - S3-E8
Continuity mistake: Homer writes '4 1/2 Reed' on his left shoe. When the owner of the music store asks him what Lisa plays, he is reading off his right shoe. (00:02:00 - 00:04:40)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: At the beginning, Mr. Burns pats his alligator, and his hand is instantly down in the next shot. (00:01:50)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Marge reveals the Christmas money from her hair, her necklace changes from red to white. (00:05:30)
Homer's Barbershop Quartet - S5-E1
Other mistake: When the Be Sharps are singing at the Statue of Liberty, in some shots the stars in the sky are black. (00:14:08)
Continuity mistake: In the video store, right after Homer picks up the tape, Maggie switches arms. (00:06:05)
Continuity mistake: Willie rips off his entire shirt before he fights the wolf, but in the next scene, when he is wrestling the wolf, he is wearing a torn-up shirt. (00:18:40)
Like Father, Like Klown - S3-E6
Continuity mistake: When Bart and Lisa see Reverend Lovejoy, their chairs keep moving closer/separating between shots. (00:13:05)
Continuity mistake: When all the salt spills out onto Milhouse's lunch, the salt that was on his food tray has disappeared. (00:10:50)
Continuity mistake: In the scene where Homer is on stage in Springfield, he's wearing shorts. When he jumps off the stage after dodging the cannon ball, he's wearing pants.
Continuity mistake: At Moe's, when Homer takes hold of the telephone its color is red, but then changes to blue as he speaks to Marge. (00:02:30)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: In Dr. Marvin Monroe's office, in the first shot, we can see a garbage can beside his desk. It disappears for the rest of the scene. The desk also moves forward. (00:13:35)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: As the family looks out the window to see the limo, the light switch on the wall has vanished. (00:03:40)
Like Father, Like Klown - S3-E6
Continuity mistake: In Krusty's story after he has his makeup washed off by a rabbi, just after his father speaks to him his makeup suddenly reappears. (00:09:40)
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