Continuity mistake: When watching the draw, the family have their TV dinners on their lap, which seem to instantly disappear between shots. (00:05:10)
Marge vs. the Monorail - S4-E12
Continuity mistake: When the sticker reveals the 1964 world fair sticker on the monorail, the world fair sticker is blue. Shot changes to a high angle shot and now the sticker is white. (00:16:40)
Continuity mistake: The way the chapstick is held out for Bob in prison changes from one shot to the next. (00:04:40)
Continuity mistake: When Lisa says she will do the pageant, her clock goes from 8:05 to 7:55. (00:08:30)
Homer's Triple Bypass - S4-E11
Continuity mistake: When we see Bart pacing when Homer is having his operation, he is on the rug in the overhead shot and by the rug in the regular shot. (00:18:50)
Homer's Triple Bypass - S4-E11
Continuity mistake: When Bart says about a train wreck near the start, the items on the table between his and Lisa's bowls changes between shots. (00:02:50)
Continuity mistake: When lying on the sofa at the start, Bart's raised leg switches between instant cuts. (00:02:30)
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)
Continuity mistake: Bart's guitar disappears when Otto starts to race to school. (00:11:15)
Continuity mistake: When we see Smither daydreaming about Mr Burns coming in through his window at night, the painting on the wall disappears between shots. (00:14:50)
Continuity mistake: During the musical number about Mr. Burns, Homer and Marge swap sides of the table. (00:05:40)
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)
Continuity mistake: When Homer tells Marge to go and get all her money, he is holding her shoulder next to her necklace. Camera changes and his hand is lower.
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: Homer rips up Bart's ticket and the bits land on the floor. Only to simply vanish into thin air. (00:15:20)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Bart is looking for food in his bedroom, he throws a book towards Santa's Little Helper. The position of this book and it's pages changes between consecutive shots. (00:08:20)
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Continuity mistake: In King Homer, When Burns is telling the reporters what the ape will be doing, the crowd in the background are devoid of any facial features. (00:11:40)
Continuity mistake: When Homer and Marge are talking about Homer seeing Lisa through a fathers eyes, the clock on the wall simply disappears. (00:08:00)
Continuity mistake: The time on the clock when Homer comes into the kitchen keeps jumping forward in massive leaps. (00:07:30)
Continuity mistake: Throughout the episode, God has 5 fingers. At the end, Homer asks what the meaning of life is, and God has only 4 fingers now. (00:21:20)
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