The War of the Simpsons - S2-E20
Revealing mistake: When Ned says "Crème de cassis" while describing what was in the drink he made. There are several animation errors in this shot. His head is disconnected from his body, and his nose disappears. Also, a part of his face is missing between his fingers while he does the 'OK' hand gesture.
Revealing mistake: When Barney is drinking beer at Moe's Tavern, his chest is, for one frame, the same color as his shirt. (00:11:30)
Revealing mistake: When Bart is hanging from the play bars his hand goes through the bars. (00:02:35)
Revealing mistake: If you look carefully in Mr. Burns' surveillance cameras, the workers are identical. (00:02:50)
Revealing mistake: When Smithers makes Mr. Burns his Wine Spritzer, Burns makes Homer Employee of the Month. While Smithers is pouring the stuff in the bottle, his left hand turns black for three frames. (00:10:30)
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.
Revealing mistake: When the car arrives at the NFI, the car goes straight through the barrier. (00:09:20)
Burns Verkaufen der Kraftwerk - S3-E11
Revealing mistake: When Homer takes out the dollar bill from his back pocket right before he puts it into the vending machine, the left side of the screen is cut off a little. You can tell especially with how the trash bin in the bottom left has a splotchy white line next to it. (00:02:20)
Radio Bart - S3-E13
Revealing mistake: At Wall E. Weasel's, when Nelson is throwing balls into the 'Skeeball' machine, the animation is repeated because Bart keeps moving in and out of the camera's view. (00:04:10)
Revealing mistake: When the announcer says that the Falcons win, he says "Who would've thunk it" Homer says "My daughter, that's who". When he is saying this, Lisa's arm disappears twice. (00:10:05)
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: After Bart gets promoted to Hall Monitor, when he tells the girl at the fountain to keep the line moving, the kid behind her drinks from the fountain but the water does not go into his mouth. (00:13:40)
Revealing mistake: On the original DVD version, when Bart says to Lisa "I didn't want you to wreck your life" the screen is cut off on the right side slightly. (00:20:25)
Revealing mistake: When Lisa is clapping erasers, you can see the alphabet above the board, and part of the A is cut off.
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: When the bartender points to the Fudd neon sign behind him, his hand goes through the sign. (00:05:40)
Revealing mistake: When Moe and Barney are seen drinking wine at the wedding, somebody walks away with a tray. When they are drinking the animation is repeated because you can see part of the tray keeps coming on and off-screen. (Look by the bottom right). (00:13:25)
Revealing mistake: When the riot police are running into the concert, you can see a 'cardboard' police officer leaning against his car, doing absolutly nothing, not even blinking or talking into his police microphone. (00:07:45)
Revealing mistake: When Skinner starts to drive the bus, he says "Off we go". During this shot the sky is a brighter colour when you look out of the bus windows than if you just look outside the bus. (00:12:15)
Bart's Friend Falls in Love - S3-E23
Revealing mistake: When Bart tells Otto not to leave due to Milhouse not being on the bus, when Otto replies you can see that his left arm up to the headphone cable flashes pink for a frame. (00:07:45)
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