Continuity mistake: When Sherri and Terri raise their hands and say "like us Mrs. Krabbapple" they raise their hands over their heads. Camera cuts and their hands are a lot lower. (00:04:20)
Continuity mistake: In the park, Marge's necklace changes from white to red. (00:15:40)
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)
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
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: 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 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: 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
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)
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: 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: When Bart is training up his army, the colours of the kid's tops keep changing between shots.
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: Homer draws a face on a punching bag. He starts to show Bart how its done. The punching bag has its eyes filled in now.
Continuity mistake: At the end when Nelson's goons are holding on to Nelson, they both have brown skin. But in the next shot, one of them goes back to having yellow skin.
Moaning Lisa - S1-E6
Continuity mistake: When Marge says, "Oh Homer, you'll lose your head if it wasn't secured to your neck," her necklace is white. However, when she gives the cup cakes to Homer and Bart, it is red. (00:02:00)
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)
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.
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.
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.
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