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)
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)
Continuity mistake: When the newspapers fall on Skinner, the rake in the corner has turned into a shovel. (00:19:10)
Continuity mistake: When Mr Burns draws the moustache and horns on the T.V. screen of Marge, they just disappear in the next shot when he starts to draw the bees. (00:19:30)
Continuity mistake: After Bart is attacked by the wolf and goes back into class, the banner above the chalkboard that has the alphabet on it is blue. Every time we see the banner after that it is yellow. (00:18:40)
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' the blue button on the toaster occasionally differs from being at the bottom of the lever to suddenly at the top, visible in the first shots of Homer fixing the toaster and between shots after Homer sits on the pink fish. (00:09:25 - 00:12:45)
Continuity mistake: When Homer drives his car to work it is lime green instead of the usual purplish color.
Tree House of Horror XII - S13-E1
Continuity mistake: At the show the school puts on in "Wiz Kids", when the Montymort Dragon is first seen in the cage, the cage has 6 bars at The Front. When Lisa says "Release The Dragon", the cage has 4 bars. When the cage door is being raised, it has 6 bars again. (00:18:45)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: As Mr. Burns and Smithers are talking on the phone, we see a hand holding the receiver, and when they're finished, the next shot shows us a black skinned referee. His skin color was yellow before. Also, the phone is nowhere to be seen. (00:15:55)
Continuity mistake: As Homer watches TV at the beginning, if you look really closely, you can see the remote on the couch colored to be exactly like brown. It then disappears eventually, and then reappears. (00:01:35 - 00:02:30)
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