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.
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)
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)
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)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When undergoing shock therapy, the doc raises his hands to his head. They are not present in the next shot. (00:19:00)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When Homer walks in on the family eating dinner, Marge has her feet on the second cushion of the sofa. Camera changes and now they are on the third cushion. (00:08:50)
There's No Disgrace Like Home - S1-E4
Continuity mistake: When they put Maggie down in the Creche she is in the middle of a carpet. Camera cuts and now she's at the edge. (00:04:25)
There's No Disgrace Like Home - S1-E4
Continuity mistake: The amount of marshmallows in the jelly at the start changes between shots. (00:02:00)
There's No Disgrace Like Home - S1-E4
Revealing mistake: When the Simpsons are eating at the dinner table, Marge's necklace keeps flashing white.
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