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
Revealing mistake: When the Simpsons are eating at the dinner table, Marge's necklace keeps flashing white.
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.
Audio problem: When Grandpa Simpson is typewriting a letter in his room, the words he's spelling out loud don't match his fingers hitting the keys.
Factual error: When Bart declares war on Nelson, Herman uses the declaration from the Franco-Prussian war and puts "Bart" in place of "Otto Von Bismarck". The thing is, Bismarck didn't declare the Franco-Prussian War, Napoleon III of France did. A small error, maybe, but something that a war buff like Herman should know.
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.
Moaning Lisa - S1-E6
Continuity mistake: When Bart and Homer first play the video boxing, the window behind them shows that it's broad daylight outside. When Homer blames his loss on Lisa's Sax, it cuts to Lisa's room and it's night all of a sudden.
The Call of the Simpsons - S1-E7
Continuity mistake: When Homer is driving through the river, in one shot while Marge is talking, Homer's vest and shirt switch colors (from green shirt and grey vest to grey shirt and green vest). (00:07:15)
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)
The Call of the Simpsons - S1-E7
Continuity mistake: When the cameraman is filming Homer in the mud, he screams quite a few times. Yet on the news report showing the footage, we only hear Homer yelling and not the screams. (00:16:00)
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)
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