Brother From the Same Planet - S4-E14
Continuity mistake: After Pepi and Tom walk off into the sunset together it cuts to Bart handing Homer another beer, and the picture behind the couch has brown sails over the boat, but next shot it's colored properly with white sails. (00:21:30)
Brother From the Same Planet - S4-E14
Continuity mistake: When Homer is showing Pepi the garage, it is purple. In the main titles and in every other episode, it is an orangey colour.
Brother From the Same Planet - S4-E14
Revealing mistake: The shot of Homer saying "Marge, when kids say bad these days, they mean good. And to shake your booty means to wiggle one's butt" is recycled from the opening scene from Life on the Fast Lane. Notice the animation is of a much lower standard than the rest of the episode.
I Love Lisa - S4-E15
Continuity mistake: When Homer and Bart are watching a clip of Sideshow Mel on wowee sauce and Bart then says "I'd give anything to go to that show", he has nothing in his hand. The shot cuts to Homer and he then says "I'd sell my first born son" and then the shot cuts back to Bart. When the shot cuts back to Bart, a Buzz cola can has appeared in his hand out of nowhere. (00:08:20)
I Love Lisa - S4-E15
Other mistake: When Lisa and Ralph are swinging at the end, they are swinging outside the frame, but the swing is tied at the top of the inside of the frame.
Last Exit to Springfield - S4-E17
Continuity mistake: When we see McBain at the beginning of the episode, after shooting some people, the magazine falls out of the machine gun. But from the next shot onwards it is back in the gun.
Last Exit to Springfield - S4-E17
Revealing mistake: When we see Lisa singing and playing the guitar for the second time, if you look to the right you can see a blue mark on the building that is behind her (On the middle turquoise stripe). It appears and disappears twice.
Last Exit to Springfield - S4-E17
Continuity mistake: When Mr Burns is telling Homer to resign, he has glasses on in the first shot in the scene. However his glasses are on his desk the next shot onwards.
Last Exit to Springfield - S4-E17
Continuity mistake: When the dentist shows Ralph the Big Book of British Smiles, he first shows him a picture of Sherlock Holmes with horrid teeth and all of his teeth are there. When Ralph starts getting terrified of it, it shows the same picture, but this time one of his teeth on the bottom right hand corner of his mouth is missing.
So It Has Come to This: The Simpsons Clip Show - S4-E18
Audio problem: When Lisa explains the origin of April Fools Day, we hear Homer, Marge, Bart and Lisa chanting "Blood For Baal." But, we see that Lisa is not taking part in the ritual and her mouth isn't moving. (00:02:15)
So It Has Come to This: The Simpsons Clip Show - S4-E18
Audio problem: After Homer puts the old milk in the fridge and Bart takes a drink from it you will then see Marge use a fork to take the milk out of the carton. Marge says "woof" but her mouth does not move in sequence with the audio.
Continuity mistake: During the Itchy and Scratchy episode at the beginning, Itchy's hammer changes from being held above him to beside him between shots.
Continuity mistake: When Roger Meyers throws his nameplate at the writer the second time, the animation is repeated from when he threw it at him earlier. It's more obvious because his mouth doesn't match what he's saying and the background is orange instead of purple like the rest of the scene.
Continuity mistake: Millhouse is in the classroom at the beginning when Principal Skinner says that superintendent Chalmers is coming for a surprise inspection, but when they show Nelson he is getting crud put down his shirt. How could he be at two places at once?
Continuity mistake: On 'Whacking Day,' Homer is seen charging people to park on his lawn. But later when the snakes are lured to the Simpson house, there are no cars there.
Continuity mistake: When the bottle of bourbon is found and taken out of Marge's pocket, the bottle is grey. But when Sanjay throws it to Apu, and Apu catches it, the bottle has now changed to a brown colour. (00:08:30)
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