Blood Feud - S2-E22
Other mistake: When Moe refills Homer's glass with beer and hands it to him, it briefly disappears and then suddenly reappears. (00:19:01)
The War of the Simpsons - S2-E20
Revealing mistake: When Maude Flanders says 'Oh, okay' to Homer after he asks for peanuts, the lipstick on her lips briefly flickers and disappears for a few frames. (00:04:56)
Tree House of Horror X - S11-E4
Revealing mistake: When Bart tells Lisa, 'Must have given you super strength,' Bart's arm is not fully coloured red and partially takes the colour of the floor from the background. (00:08:25)
Revealing mistake: When the dog attacks Chief Wiggum, you can see a floating flashlight, a person in the bottom right corner missing an eye, and a cameraman pointing the camera elsewhere instead of at the ground. (00:04:54)
Revealing mistake: When Mr. Burns tastes the burger, his ear briefly turns the colour of his hair. (00:04:25)
Much Apu About Nothing - S7-E23
Audio problem: When they shout 'No on 24!', none of the people move their lips. (00:21:03)
Three Gays of the Condo - S14-E17
Revealing mistake: When Homer says to Smithers, 'It's so manly, but scented,' Smithers' mouth disappears for one frame as he laughs. (00:10:47)
Homer Badman - S6-E9
Other mistake: When chasing Homer and Marge after the theft of the gummy Venus de Milo, some of their pursuers run on vertically positioned tables instead of the ground. (00:05:07)
We're On the Road to D'ohwhere - S17-E11
Continuity mistake: When Lisa tells Marge that Flanders has only bought his own, and as the zoom pulls back to focus on Flanders, Lisa's mouth abruptly opens in one frame and then shuts very abruptly in the next.
Continuity mistake: When Mr. Bergstrom and Homer are eating together, Mr. Bergstrom's left hand is up and holding a fork, but the next shot shows his left hand resting on the table.
Continuity mistake: The long shot of Homer and Mr. Bergstrom eating lunch together at the childrarium shows Mr. Bergstrom's left hand resting on the table, but the next close-up shot of the duo shows Mr. Bergstrom's left hand up, holding a fork.
Continuity mistake: As Homer speaks with Apu before the robbery, Homer has a fudgesickle in his left hand, but when he turns from Apu to leave, the fudgesickle disappears.
Continuity mistake: When Homer tells Lisa he needs "daughter's picks" while he's watching the playoffs, Lisa tucks the pencil behind her ear with its point facing her back, but in the next shot the pencil is tucked the opposite way with its point facing her front.
Continuity mistake: After the Simpsons are selected for the 1895 reality show, they're shown the video confessional room, with the only tech in the house. When Marge is in this room confessing about her blue hair, the doorknob is on the right, but when Bart is inside confessing that he's miserable, the doorknob is on the left side of the door.
Continuity mistake: When Homer brings his family to Lenny's apartment, as Lenny shuts his front door, its doorknob is on the right, but when Homer and his family depart Lenny's crazy apartment, now that front door opens the opposite way, with its doorknob on the left.
Continuity mistake: When Marge opens the dishwasher and tells Lisa to reattach the toilet seat, there's a red dish rack on the counter over the dishwasher, but in the previous and following shots there's a filled casserole dish over the dishwasher, not a dish drying rack.
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.
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