Audio problem: When the car drives into the cornfield, Martin is heard screaming, even though he is still asleep.
Continuity mistake: In the overhead shot of Patty smoking, she is sitting on a greenish-gold car, the car then turns blue in the next shot.
Continuity mistake: When Homer gets up to make Mr. Burns' breakfast, Marge's nightgown is yellow, making her look naked, but in the next shot, her gown is purple.
Continuity mistake: At the funeral, while everyone is clapping for Bob Newhart, Mayor Quimby is seen with brown skin.
Scenes From a Class Struggle in Springfield - S7-E14
Audio problem: Homer's mouth is completely out of sync when he says "our savings?"
Team Homer - S7-E12
Revealing mistake: When the children are running down the hallway, the animation keeps repeating. Duplicates of the same children are running several times.
Three Men and a Comic Book - S2-E21
Audio problem: When Homer offers to take the family to Krusty Burger, Lisa is heard cheering, even though her mouth is closed.
Ned 'N' Edna's Blend - S23-E21
Revealing mistake: When Marge is talking to Helen Lovejoy about Canapés at the party, Marge's mouth disappears for a single frame.
Continuity mistake: After Moe yells at Ralph, there's a woman in the background staring at Moe with an angry look on her face. She turns her head away from him after some seconds, but in the very next shot, she is looking at Moe with the same expression on her face.
Continuity mistake: When Milhouse snitches on Bart, Martin has grey hair and a black suit. In the very next shot he has his ordinary hair and is wearing a brown suit.
Continuity mistake: Jasper's beard is missing when everyone is singing "In-A-Gadda-Da-Vida" at church.
Springfield Connection - S6-E23
Revealing mistake: Homer's hand briefly turns transparent when he puts it on Marge's shoulder after he tells her to rip up the ticket.
Springfield Connection - S6-E23
Continuity mistake: While the Simpsons are eating breakfast, Lisa is eating what seems to be cereal from a bowl, but when she asks Marge if she needs to take a bullet for the mayor, she now has a plate in front of her with eggs and some other food.
Springfield Connection - S6-E23
Continuity mistake: The clothing of the women at the hair salon (Maude, Agnes, and Mrs. Krabappel) keeps changing color throughout the entire scene.
Revealing mistake: Mr. Burns' body is not seen through the window of his car when he tells Smithers to drive.
Homer vs. Patty and Selma - S6-E17
Revealing mistake: While the Simpsons are having dinner, the top portion of the chair Homer is sitting on disappears when he tilts the chair back.
Lisa on Ice - S6-E8
Revealing mistake: While Bart and Lisa are skating off the ice rink, the skin color of one of the people in the background during the riot keeps flashing yellow and brown.
Revealing mistake: When all the students are leaving Springfield Elementary after the fire alarm is pulled, the same students keep passing over and over again.
Revealing mistake: The people waiting in line for the game are extremely crude drawings. Some of them aren't even completely drawn, e.g, some are missing arms, legs and other body parts.
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: When the Simpsons are leaving the house to go to the mall. The aerial shot shows that they are leaving in Marge's red station wagon, but the very next shot of them in the car shows that they are in Homer's pink sedan. The shot of the station wagon leaving is probably a re-used shot from a previous episode.
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