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.
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.
Scenes From a Class Struggle in Springfield - S7-E14
Revealing mistake: When Lisa is first shown riding the horse, the horse's eye is colored solid red.
Revealing mistake: When Lisa is explaining to the curator of the museum why she didn't tell the crowd of what she learned about Jebediah Springfield, if you look in the background none of the people on the far sidewalk are moving, almost frozen in place with some of them with their arms in the air yet everyone and everything in the parade keeps moving right along.
22 Short Films About Springfield - S7-E21
Revealing mistake: A black line briefly appears on Apu's forehead while he's tossing the tofu dog around.
Revealing mistake: While Larry and Homer are talking about Mr. Burns, Larry's drink flickers light pink twice.
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious - S8-E13
Revealing mistake: When Dr Hibbert is examining Marge's hairs (and I think another time in the episode), some holes are too low and you can see through her head.
The Old Man and the Lisa - S8-E21
Revealing mistake: At the hospital, while Lisa is explaining how much 10% of $120 million is to Homer, Dr. Hibbert's hand is yellow.
Revealing mistake: When Lenny is talking about Homer not needing a degree to work at the power plant, Lenny's five o'clock shadow briefly detaches from his face.
The City of New York vs. Homer Simpson - S9-E1
Revealing mistake: Homer drives his car through the man at the picnic.
Revealing mistake: When Skinner talks to Otto on the bus, the point of his hair is touching a pole. Look at the pole - Skinner's hair is going through it.
Revealing mistake: At the U.N. meeting, Bart places his glasses down on the table to read out the Libyan exports. As he puts the glasses down, you can see they are unrealistically floating in the air.
Revealing mistake: In the scene where Marge is cutting Grampa's hair, his left cheek in the mirror's reflection turns blue.
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