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
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
Continuity mistake: Bart yanks Homer's beard off in the mall, Homer then takes Bart into Santa's workshop. When they are inside Santa's workshop, Homer's beard is back on, despite the fact that he let it fall to the ground when Bart pulled it off.
Moaning Lisa - S1-E6
Continuity mistake: Marge drops Lisa off at school for band practice. She walks up to the entrance steps, and then converses with two boys. Then her teacher comes up, and Marge gets annoyed. When she comes to grab Lisa back into the car, Lisa is right by the roadside, along with the two boys and the music teacher.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Mr. Burns comes on the P.A. system Homer started eating a donut, he takes a bite and after that the donut stays the same size even though he takes 2 more bites. (00:06:40)
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)
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 the cops pin Krusty to the carpet, he moves further away from the yellow stripes between shots.
Continuity mistake: When Bart's army is attacking Nelson, there are a lot more kids attacking Nelson than there were training with Bart.
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."
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)
Moaning Lisa - S1-E6
Continuity mistake: When Homer says "I can't concentrate with that infernal racket", the shot goes up onto Lisa's room. From the outside, there is no window frame on the window. But from the inside, there is one going right through the middle.
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.
Continuity mistake: The whole family goes to the opera to see "Carmen". They have balcony seats and the stage is to their left, yet later on you can see them looking to their right.
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)
Continuity mistake: At the start, when Nelson takes the cupcakes, you can see that after he has started eating them there are 4 left in the box. Just before he shuts the lid to drop it, you can just see the tops of 6 cupcakes.
Continuity mistake: In the initial robbery at the Kwik-E-Mart, Apu doesn't realise what's going on until the fake Krusty demands the money from him. Yet in the video shown in court, he turns to face the fake Krusty right as Homer screams.
Continuity mistake: At the very end of the episode, when Homer is being carried off by the crowd, you can see that the crowd carrying Homer, the people are small, so you'll have to look closely, but right before the credits, Marge's necklace changes from red to white, back to red and then finishes with white all in one shot. (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