Revealing mistake: When Homer pushes over the windmill something comes off and chops the head off a metal figure, but the head comes off before hit. (00:16:05)
Revealing mistake: When Marge stands up at one point in the airplane restaurant, her legs and part of her dress have disappeared.
Revealing mistake: When Marge says, "Slow and steady wins the race", her face and body are two different colors.
When You Dish Upon a Star - S10-E5
Revealing mistake: At court, as Homer is walking towards Alec Baldwin, Kim Basinger and Ron Howard, Bart is in the background sitting with the rest of the Simpsons, but his head is missing from his body. His head then reappears back on his body after about 2 seconds.
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 Lisa is daydreaming about her failed test, the president of Harvard talks to her. When he says, "Nasty business that zero", his right white sleeve turns the same color as the glass above the door.
Revealing mistake: When Nelson is offering Lisa the fraction quiz answers, right before Lisa says she's never cheated before and won't again, her right hand disappears for a single frame.
Revealing mistake: Two kids in the middle of the class do not have a test. However, they are shown writing on their desk as if they had a test paper.
Revealing mistake: When Fat Tony says,"I am not so much disappointed as I am blinded with rage", the dark circles under his eyes disappear for a split second.
Wild Barts Can't Be Broken - S10-E11
Revealing mistake: Lenny's lower torso disappears for two frames when he, Carl, Homer and Barney are singing "We Are The Champions/We Will Rock You."
Revealing mistake: There are two Ruth Powers in the same shot, when the people are crowding on Homer at the mall.
Revealing mistake: After Apu and Manjula go by in horse and cart everyone returns into Moe's. When they walk in they just disappear into a brown wall which is where the inside of Moe's should be seen.
Revealing mistake: When Homer says "Oh, baby we got him now" whilst arriving in the airport, you can see half of Doctor Hibbert's face in the background, but you can see he doesn't have any eyebrows or eyes.
Revealing mistake: When Homer is giving Marge, Lisa and Bart money, Homer puts his hand on Bart's shoulder and whispers 'Mel's movie really stinks'. When he lets go of Bart to say this, he leaves his fingers on Bart's shoulder, but he still has fingers on his hand.
E-I-E-I-(Annoyed Grunt) - S11-E5
Revealing mistake: After Lisa says "For a product that's evil and deadly" while standing in front of the tomacco stand, there's a duplicate Lisa behind her that stands still while she moves, giving Lisa the appearance of having two heads. It looks like the animators made a mistake while trying to animate Lisa.
Revealing mistake: When Lisa wraps herself in Marge's arms right before she falls asleep, the inside of her mouth turns yellow.
I'm Goin' to Praiseland - S12-E19
Revealing mistake: In one of the scenes (I think it is when they first discover the alleged 'miracle') you can see people in the background walking out of the park. But they are not walking out of the park at all, they are walking into the wall.
Little Girl in the Big Ten - S13-E20
Revealing mistake: When Bart says "I don't feel so good" after being bitten by a mosquito, his lower body under the table is not visible.
Don't Fear The Roofer - S16-E16
Revealing mistake: When Homer sits on Lenny's cake in Moe's bar, some of the frosting appears to stay in mid air, and when the frosting is on the wall, it doesn't slide to the ground like frosting would.
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)
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