Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: In Dr. Marvin Monroe's office, in the first shot, we can see a garbage can beside his desk. It disappears for the rest of the scene. The desk also moves forward. (00:13:35)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: During the 'Next week, on the Simpsons' clip, Maggie changes where she sits at the table. Lisa also changes where she sits, as you can see in the background. (00:21:45)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Jimbo and Kearney take Homer's candy, it is obviously night time. However if you watch the outside as Homer closes the door before he says "Lousy punks" it shows a daytime sky.
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Mr. Burns is telling the robot Homer that he is his daddy, Burns is to the right of Homer, but after the POV of Burns' face (he is still oriented right of Homer) by Homer, Burns is now to the left of Homer.
Lisa's Pony - S3-E8
Continuity mistake: Homer writes '4 1/2 Reed' on his left shoe. When the owner of the music store asks him what Lisa plays, he is reading off his right shoe. (00:02:00 - 00:04:40)
Lisa's Pony - S3-E8
Continuity mistake: The people sitting behind Marge during the talent show keep changing/disappearing. (00:02:10 - 00:06:00)
Lisa's Pony - S3-E8
Continuity mistake: The number of knives that Sherri is holding changes between long and close shots at the talent show. (00:04:50)
Lisa's Pony - S3-E8
Continuity mistake: Homer's digital watch disappears when he enters the auditorium. It also vanishes in the first shot of Homer in the music store. (00:05:05 - 00:06:25)
Lisa's Pony - S3-E8
Continuity mistake: During Lisa's performance, In one shot of the audience we see, from left to right: Ned Flanders, Maude Flanders and some lady. The rest of the talent show showed us that Jasper was sitting where the lady was. (00:05:45)
Lisa's Pony - S3-E8
Continuity mistake: After Homer watches the tape, Marge suddenly appears beside him. (00:07:30)
Lisa's Pony - S3-E8
Continuity mistake: In the last shot of Marge and Homer's discussion of buying a pony, we can see a door on the right side of the screen. This door changes position when Lisa rides in the bedroom with her pony. (00:08:45 - 00:12:10)
Lisa's Pony - S3-E8
Continuity mistake: When trying to get a loan, Homer is tapping his fingers on the counter. When the shot changes, his hands are by his side. (00:10:00)
Lisa's Pony - S3-E8
Continuity mistake: When applying for the loan, a bell appears on the counter in front of Homer. (00:10:00)
Lisa's Pony - S3-E8
Continuity mistake: In the kitchen, there is a clock on the wall that changes time from 07:10 to 09:10. (00:12:10)
Lisa's Pony - S3-E8
Continuity mistake: Before Lisa licks the salt lick, there is another horse in the stable which disappears. (00:14:30)
Lisa's Pony - S3-E8
Continuity mistake: When Ralph is sat on the fence watching Lisa, his position changes between shots. Note the fence post in relation to his body. (00:15:20)
Lisa's Pony - S3-E8
Continuity mistake: When Lisa calls Homer at work, Homer picks up the phone on his left side. Instantly after, we see him hang the phone up on his right side. (00:19:00)
Lisa's Pony - S3-E8
Continuity mistake: When Homer is phoned by Lisa, the color of the phone is blue. Immediately after, it turns to green. (00:19:00)
Lisa's Pony - S3-E8
Continuity mistake: At the end, the melted cheese and work outfit disappears from Apu's hands. (00:21:20)
Lisa's Pony - S3-E8
Continuity mistake: At the very end, the outside of the Kwik-E-Mart is different. (00:21:35)
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