The Mook, the Chef, the Wife, and Her Homer - S18-E1
Revealing mistake: When Fat Tony says "The Calabresis. My archenemies in waste management." while driving the carpool, a huge line briefly appears around his cheek and mouth.
Continuity mistake: The time on the clock when Homer comes into the kitchen keeps jumping forward in massive leaps. (00:07:30)
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: 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)
Revealing mistake: Krusty's nose flashes white for a split second during his song for the winner of the Little Miss Springfield pageant. (00:15:06)
Continuity mistake: When talking to the family about no longer attending church, Bart moves behind Homer in an instant cut. (00:07:45)
Revealing mistake: When Lisa says "Truly this was an act of God", her ear disappears and reappears several times. (00:19:30)
A Streetcar Named Marge - S4-E2
Continuity mistake: When Maggie fires the dart onto the locker, it's position in relation to the vent slits changes between the long and close up shots. (00:14:30)
22 Short Films About Springfield - S7-E21
Other mistake: When Chalmers and Skinner are having lunch with hamburgers, Chalmers bites it. When he opens it, the bread's slice is bitten but the meat is not.
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Moe opens the special Duff and foam appears down the bottle that disappears instantly. (00:05:10)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: After the Germans have bought the plant, Homer takes a bite of his doughnut. The bite changes size between shots when Lenny and Karl ask him why he can't be fired. (00:09:10)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When the two Germans are looking at Homer in Moe's, the one's hand is on his paperwork. Camera cuts and it's half off the paperwork now. (00:05:20)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Homer pours his bottle of beer into his glass creating foam that is raised above the lip of the glass. Camera cuts and the foam has gone. (00:05:20)
Other mistake: When Moe is calling for a 'Hugh Jazz' there is a shot of the bar and Otto can be seen in the upper right corner. However his face is all distorted and out of proportion. (00:14:30)
Continuity mistake: When Moe gets up on stage with Aerosmith you can see the big "Flaming Moe's" sign behind them. However in the close up the sign isn't visible. (00:13:30)
Continuity mistake: When Homer is smelling the BBQ the smoke that's in front of him vanishes instantly. (00:03:30)
Continuity mistake: The paper that Bart draws Skinner on changes from ruled to plain. (00:14:00)
Other mistake: When watching TV at the start Homer's beer can just says D instead off Duff. (00:02:15)
Continuity mistake: When Bart gets off the bus there is a fire hydrant behind him. When we see the bus drive off the hydrant has gone. (00:07:10)
Continuity mistake: When Bart gets on the bus the day of the test, Milhouse is sitting at The Front of the bus. When we see Sherri and Terri looking at Bart, Milhouse has gone. (00:06:30)
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