Three Gays of the Condo - S14-E17
Revealing mistake: When Homer says to Smithers, 'It's so manly, but scented,' Smithers' mouth disappears for one frame as he laughs. (00:10:47)
Revealing mistake: When Homer leaves the bar after the Superbowl, as he goes through the door, the background is missing. It's just a brown background. (00:20:00)
Revealing mistake: When Grandpa is reading from the book trying to find out what is wrong with Maggie, the pages are blank. (00:09:30)
Itchy and Scratchy: The Movie - S4-E6
Revealing mistake: When Lisa is trying to explain to Homer about Bart seeing the movie, one of the pearls on her necklace keeps disappearing and reappearing. (00:18:20)
Revealing mistake: When the car arrives at the NFI, the car goes straight through the barrier. (00:09:20)
Revealing mistake: While Homer is waiting for Marge to come downstairs, both Patty and Selma are wearing turtlenecks. When Homer thanks Mr. Bouvier, in the next wide shot as the twins nod their heads, both of their turtlenecks are not colored in properly at their torsos, so the background is visible through their bodies. (00:16:30)
Itchy and Scratchy: The Movie - S4-E6
Revealing mistake: When Marge says she's sure Bart doesn't mean to be bad, her necklace flashes through her neck. (00:03:40)
Revealing mistake: At the start when we see stuff falling off the roof, the animation for the swings in the background simply fade out and are incomplete. (00:02:05)
Revealing mistake: When the bartender points to the Fudd neon sign behind him, his hand goes through the sign. (00:05:40)
Revealing mistake: When Homer is putting up all the lost dog posters on the building that gets blown up, the stapler isn't on the poster. (00:17:30)
Revealing mistake: At the circus as the clowns appear you can see a composition error on Homer's body. Homer's body is indexed to be as a background scene for several seconds where you can see the man's head fully who is sitting in front of Homer but you can just see that the man's head is in front of Marge's body. You will also see the clown's shoes walk over Homer's body before they update Homer's body correctly. (00:05:19)
Revealing mistake: In the opening sequence's parody of the series where Bart becomes fat and comes out from school on his skateboard, he theoretically should go down the stairs, instead his silhouette suddenly climbs up on the wall next to him, revealing a mistake in the post-production's animation. (00:06:05)
Revealing mistake: During the intro to some earlier episodes where Bart leaves the school, the scene pans down and the edge of the animation paper can be seen in a couple spots at the very bottom of the frame. It is blue in color. This error persisted through many seasons.
Revealing mistake: When Bart is hanging from the play bars his hand goes through the bars. (00:02:35)
Revealing mistake: When Marge stands up at one point in the airplane restaurant, her legs and part of her dress have disappeared.
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: When Moe grabs Ned Flanders' shirt at the bar, Ned's torso is incorrectly drawn over his arms as well as the mug he is holding. (00:10:50)
Lisa's Pony - S3-E8
Revealing mistake: At the end, Homer and Lisa don't cast a reflection on the Kwik-E-Mart's doors. They should, since they are only a few metres from it.
When You Dish Upon a Star - S10-E5
Revealing mistake: When Homer and the family are having hamburgers at the dinner table, at one point you can see the oven. The pointer on one of the dials is misaligned.
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.
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