Continuity mistake: When Mr. Burns realises just how much Grayson is adored by fans, Warburton Parker has multiple bracelets on his right wrist, but in the next shot as Parker tells Burns about the media-driven world, his bracelets have vanished; then after Smithers opens the floor's trapdoor, Parker's bracelets reappear as he falls through the trapdoor.
Continuity mistake: During the episode, Grayson Mathers wears a watch on his wrist that inexplicably vanishes and reappears a few times. First, when Marge is in the school infirmary with Grayson, as he says, "I called Peyton Manning a chicken-fried Frankenstein." Second, when Grayson and Bart tussle after family dinner, and Marge tells them to behave. Third, when Mr. Burns shows up at Grayson's birthday party.
Continuity mistake: When Moe pours Pinot Noir into two wine glasses for himself and Maya, Moe's wine glass vanishes from his hand when Barney shows up. Then, when Maya acknowledges that she and Moe are definitely an item again, Maya's wine glass vanishes from her hand. Lastly, the wine bottle vanishes from Moe's right hand between shots as well.
Continuity mistake: When Moe and Maya are in the bar's back room, Moe feels like singing. At the start of this scene, there are dresses with criss-crossed straps hanging on a clothing rack, and those straps are facing the couch. As the scene progresses, changes occur: first, the criss-crossed straps face the opposite way, and then those straps disappear altogether, etc.
Continuity mistake: When Moe brings Homer to the alley outside to talk about "Midge" and his fear of losing Maya again, they go through the bar's back door, and that door's window vanishes in the following shots.
Continuity mistake: A random woman asks Homer to be her baby's godfather, and he declines. When it cuts to Moe's bar, the bar's front door opens either at its left or its right, depending on the shot. This occurs again later when Moe returns to the bar to speak to Maya.
Continuity mistake: When Ralph says, "Climate change is real," both of the cars are in the driveway, the Simpson family stands on the sidewalk, and their mailbox is gone, but after the family's close-up both cars have vanished, they're all standing on the grass, and their mailbox reappears in its proper place.
Continuity mistake: While Moe drives his car during the traffic jam, the car's rearview mirror repeatedly vanishes and reappears.
Mothers and Other Strangers - S33-E9
Continuity mistake: A teenage Homer and his father travel to Utah to look for Homer's fugitive mother, whom they find. This completely contradicts the episode Mother Simpson, where Homer didn't reconnect with his mom until he was in his late thirties, and was told all his life by his father that she was dead, even believing that the grave of Walt Whitman belonged to his mother.
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