The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: Lewis changes from black to yellow when Milhouse dares Bart to pull Santa's beard off. (00:14:10)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: After Homer brings Santa's Little Helper home, Homer and Marge hug, and if you look behind them, the background is upside down. There is a picture hanging upside down, and there is a lamp which seems to be hanging from the ceiling. Then in the next shot, the background is normal. (00:21:40)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: While having breakfast, all of the Simpsons' glasses of orange juice keep disappearing and reappearing throughout the scene. (00:05:35)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer walks out Circus of Values with his purchases, he bumps into Flanders, and all the presents scatter everywhere. Watch out for a red present with a green bow that goes flying near the left hand side of the screen. As soon as it hits the ground it turns into a pink box with a white bow wrapped around it, with no shot changes. (00:10:15)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: When Marge is speaking on the phone to her sisters, her sisters say something that sounds like they said that Homer is ugly. Marge then puts down the phone wire that she was curling round her finger. You can temporarily see that the phone wire disappears when Marge puts it down. It is at the very end of an early scene, because as soon as this happens it changes to another scene. (00:04:40)
Factual error: After Bart's prank call with Moe, you can see Bart and Lisa laughing. However the telephone's wire does not connect to the receiver. (00:09:40)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: Marge walks through the doorway from a room with a piano, beside a bare wall, and on the piano are two frames and music sheets. But when Marge turns the jar upside down, there is a large picture on the wall beside the piano, and the music sheets and frames have disappeared from the piano. (00:08:00)
Revealing mistake: During the first ten minutes when the twins are explaining to Bart what incompetence means, one of the twins' body disappears, showing a floating head and hair. (00:06:30)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer finds out that he has no Christmas bonus the background behind Marge is the kitchen, but then it cuts to Homer and the background behind him is the kitchen too. (00:08:20)
Continuity mistake: When Sideshow Bob is shouting and screaming just before he is taken away in a police van, Lisa and Bart swap places right before Bart says "Take him away, boys."
There's No Disgrace Like Home - S1-E4
Other mistake: When Homer is at Moe's, there is a boxing match happening on TV. There is a bald guy who is getting considerably battered by the opponent and gets knocked out, and then for some absurd reason he is victoriously standing and smiling as if he had won.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: During the family's breakfast, in most shots Marge sits right beside Maggie's highchair, but in certain close-ups they are quite a few feet away from one another. (00:05:25)
The Call of the Simpsons - S1-E7
Continuity mistake: When the bear first confronts Maggie, she is on a path. Yet in the next shot when the bear lands on the ground, she is on grass. (00:11:15)
Continuity mistake: When Bart is explained the answer RDRR, there is a shot of him. There is a blue background where the classroom should be.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer and Flanders drop their presents, the presents move around and change colours between shots. (00:10:20)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Millhouse, Bart and Lewis are talking about the fake Santa, Millhouse's eyebrows go from blue to black to blue again. (00:14:15)
Continuity mistake: When Bart and his friends are making copies of the photo of Homer, the banner across the copier says "Copies 5 cents," but when they go to deposit the money it says 10 cents.
Continuity mistake: While Bart starts the I.Q. quiz and is reading it out loud, his teacher says "Shh. Visualize it Bart." While this happens if you look in the background you can see the alphabet line. It starts out Tt Uu Vv Ww, then Bart's teacher blocks out some, then you see the letter T again. (00:04:50)
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: At work, the salad in Homer's sandwich disappears when he mentions that 'she' made it.
Continuity mistake: When Homer and Bart are at the cabaret show, Mr. Burns and Smithers are there with two women. In almost all of the shots there is a woman sitting between Burns and Smithers, except in the close-up of them when Burns asks "How does he DO it?". Then Smithers is shown as sitting right next to Mr. Burns. (00:21:00)
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