Revealing mistake: When Bart is watching Rod and Todd walk over to Ned Flanders, you can see their reflections on Bart's telescope. Their reflections do not match their actual positions.
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.
Lisa on Ice - S6-E8
Revealing mistake: After the buzzer goes on the final game and the crowd reacts one of the crowd members says "Tie Game.", then some woman in a red top says "What the Hell.". If you look at the woman when she moves her head you can see the nose on her face disappears. (00:19:55)
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.
Homer Badman - S6-E9
Revealing mistake: In the scene where Marge's coat pocket bursts open, the candy flows onto the floor. However if you look to the right of her some of the candy seems to almost float above the floor. The candy's direction is completely to the right but because of the floor being angled it spreads over one woman who is standing and there is nothing there to support the candy. (00:04:30)
Grandpa vs. Sexual Inadequacy - S6-E10
Revealing mistake: When Doctor Hibbert drinks the bottle of tonic, the amount of tonic never actually changes even though it should have gone down a considerable bit.
Revealing mistake: In the scene where the family is in the car, driving home from The Town hall meeting, Homer says "the whole reason we have elected officials is so we don't have to think all the time!" When he says "don't" a second collar appears beneath the right collar of his shirt, and then disappears after he says "time." (00:11:20)
Revealing mistake: When a comet is about to hit Springfield, everyone is standing on a hill in the shadow of it. But the shadow is still there even after it breaks up.
Revealing mistake: When everyone is in Ned's shelter, the woman in the top left hand corner with brown hair and brown skin briefly has 2 pupils in each eye.
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.
Revealing mistake: When Lisa and Hugh go by Taxi to the Simpsons house, you can see that they pass the same buildings all the time, especially "Coffee shop".
Revealing mistake: By the end, when fortune teller lays "The Fiance" card on the table, it instantly makes the same angle as other cards lying there, even though the teller's hand is still under it. It doesn't change the angle when she removes her hand from under it, as though it's floating in the mid-air all the time.
Revealing mistake: During Skinner's speech to the students in the school cafeteria, two Allison Taylors are seen sitting on different sides of the cafeteria.
Revealing mistake: Mr. Burns' body is not seen through the window of his car when he tells Smithers to drive.
Springfield Connection - S6-E23
Revealing mistake: Just after when Marge is reading the book on the sofa she says 'chaos'. On the far left of the screen a large black 'scratch' appears then just slides off.
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.
Who Shot Mr. Burns? (1) - S6-E25
Revealing mistake: Right at the beginning, watch as Principle Skinner enters the classroom, there's a clock on the top left hand of the screen. The majority of the left side of the clock is not drawn in.
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