The Call of the Simpsons - S1-E7
Revealing mistake: The scientist who describes Homer as a brilliant beast seems to have some of his hair magically floating above his ear - it's not connected to his head, yet it moves alongside his head. (00:20:40)
There's No Disgrace Like Home - S1-E4
Continuity mistake: As Homer is carrying the TV towards the pawn shop in the first shot the left window is clear. There is then a tracking shot of the family walking and when they get in front of the store the window has writing on it saying Pawn Shop. The writing is in black and the next shot when they are talking the writing is now dark brown. (00:14:20)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer walks up The Front drive you can see the road and there are no markings on it. But when he turns to look at his house, there are orange lines running down the road. (00:08:50)
Moaning Lisa - S1-E6
Continuity mistake: When Marge is driving Lisa to school, in one shot you can see that her necklace is red. Then in the next shot it is white. It then changes back to red and stays that way.
Continuity mistake: In the park, Marge's necklace changes from white to red. (00:15:40)
There's No Disgrace Like Home - S1-E4
Audio problem: When Marge gets drunk at the picnic, she falls on Homer while saying "Homie, did you try the punch?", her lips don't move. (00:06:20)
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.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Audio problem: When Homer is putting Christmas lights around the outside of the house, he falls from the roof. You can then hear Lisa and Bart sarcastically clap. But you can see they both have their hands by their side, and no-one is clapping. (00:04:55)
Continuity mistake: When Marge is throwing all the Krusty merchandise into a bag, the bag changes from grey to brown between shots.
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.
Moaning Lisa - S1-E6
Continuity mistake: When Homer and Bart are playing video boxing for the first time, the interior of the living room keeps changing. (00:06:00)
Continuity mistake: When Bart is training up his army, the colours of the kid's tops keep changing between shots.
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.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Jacques is trying to seduce Marge at Barney's Bowlarama, the ball he is holding is coloured purple. When we see him a little later on, he is now carrying a green ball.
Continuity mistake: When Homer reaches into the fridge to take out the tub of triple chocolate ice cream, we see it in a brown and white striped tub. When he lifts it out, it's turned into a plain pink tub and has shrunk considerably. (00:03:50)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer has been informed about the Christmas money being spent on Bart getting his tattoo surgically removed, he leaves the house. When he opens and closes the door to leave, the wreath on the door is white with a red bow. When Homer then turns to look his Christmas decorations, the wreath is now green. (00:08:50)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When the Simpsons are spying on the old man, the boy and the old woman, all three of them disappear and then reappear between shots. Whenever there is a wide shot from outside the house, they are not there but when there is a close shot from outside or inside they are there. (00:11:00)
Continuity mistake: When Bart enters the tree house after being beaten up, he puts his hat on a peg behind him. In some later shots at an angle you can just see the hat behind him. In the shots from directly in front of Bart, the hat is not on the peg.
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.
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