A Streetcar Named Marge - S4-E2
Continuity mistake: As Marge is about to leave for her first audition, she walks across the room and she is wearing white slip-on shoes. Then her and Homer talk for a bit, then when it cuts to a wider shot after they talk, she now has her red flat-heels on. (00:03:30 - 00:04:00)
A Streetcar Named Marge - S4-E2
Continuity mistake: Just as Marge heads out for her 1st audition, the kids go from lying on the sofa to sat up instantly. (00:03:35)
A Streetcar Named Marge - S4-E2
Continuity mistake: When Marge walks across the living room she has a bag in her hand which disappears when the camera changes. (00:03:35)
A Streetcar Named Marge - S4-E2
Continuity mistake: Otto's tattoo changes from the close up and the long shot of him when auditioning for Stanley. Note the eyeballs. In the first shot they are past the top hat. In the following they are much further back. (00:05:30)
A Streetcar Named Marge - S4-E2
Continuity mistake: When Homer picks up the snacks from the vending machine, 2 items are left on the floor. When Marge is practising her lines a few shots later, the items have disappeared. (00:11:10)
A Streetcar Named Marge - S4-E2
Continuity mistake: When Maggie is looking down at the desk to see the keys, there is a book on the desk as well. When she's looking down at the adult walking into the room the book has gone. (00:14:00)
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)
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