Continuity mistake: After Lisa unlocks the bathroom door with the coat hanger, the puddle of "baby blood" (Pepto-Bismol) at her feet disappears in the next shot.
The Trouble With Trillions - S9-E20
Continuity mistake: In the post office when Chief Wiggum is using the megaphone, Otto is seen in the right line as seen from the door but when Kent Brockman attempts to interview him he is magically in the other line, in front of Krusty.
Kamp Krusty - S4-E1
Continuity mistake: Bart holds up his maths book but in the next shot the book is on the desk. (00:05:00)
Continuity mistake: When Moe is wiping the beer glass at the beginning of the episode, the glass is initially smooth but changes to dimpled in the very next shot.
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Audio problem: In King Homer, after Burns and the guards on the island rush through the doors, you hear Burns say "Shoot him in the groin and belly!" But his mouth doesn't move. (00:10:30)
Elementary School Musical - S22-E1
Other mistake: As Stephen Hawking rotates in circles, his front wheels stay locked in a straight position, rather than turning into the turn.
Elementary School Musical - S22-E1
Other mistake: As Lisa and Marge drive out of Brooklyn, they see a mural painted by the two artists. As the camera looks at Lisa, the mural reflection should be reversed, but isn't.
Continuity mistake: When the students have to practice square dancing in the gym, Lisa spots a male student and there is a red circle next to her on the floor where she is standing. When the teacher tells Lisa she has to dance with groundskeeper Willie, the circle has disappeared.
Continuity mistake: When Lisa arrives home after her parents gave the boy a party, she parks her bicycle near the path. When Lisa sees the boy with make-up on his face in the next shot, the bicycle is on the grass.
Continuity mistake: When Lisa and Tumi are listening to the radio in Lisa's bedroom, the door behind them changes position between shots.
Continuity mistake: When Lisa and Tumi have finished their square dancing, there is nothing to the left of the basketball stand, but when Lisa and Tumi are talking in the next shot, three balls have appeared.
Continuity mistake: When Homer reveals the murderer in the story, he is holding a card in his right hand. When Booth tells Homer he has given away the game, the card has disappeared.
Continuity mistake: When Marge and Maggie check out their groceries at the supermarket, the cashier says that she requires a price check on Gramma Shortcut's Store Bought Bundt Cake. The position of the cake on the scanner changes between shots.
Continuity mistake: In a full view of the checkout, when the cashier requires a price check on Gramma's Shortcut Store Bought Bundt Cake, you can see beside Marge there is a stand and there is a man with a beard and glasses behind it. When we see Marge in the next shot, the man is now standing behind her, and there is also a couple who weren't there previously.
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