I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: When the boys get to the top of the hill the light on The Front of the bike has shrunk dramatically since the first time we saw it at Bart's driveway. (00:00:55 - 00:02:15)
Audio problem: When Homer sulks about not knowing anything about Bart, his first words of speech doesn't match his mouth. (00:08:20)
Continuity mistake: As soon as the family has left the Knowledgeium, they are immediately outside walking away. The shot changes and the building is nowhere to be seen.
Audio problem: When Bart is reading Marge's police file he says 'Oh, Mum's only been in twice.' But the lip sync is a bit out because it does not match the words he says.
Factual error: As Bart, Homer, Ned and Todd drift away from land in their boat, we see the clouds moving away. The clouds would not move that fast at the speed that the boat was going.
Continuity mistake: During the 'whose garter is this?' joke Patty and Selma appear behind the Simpsons. (00:20:10)
The Fat and the Furriest - S15-E5
Continuity mistake: When Homer realises that the bear was only agressive because of the electrical tag, they share a bear hug. The back of Homer's shirt is torn to tatters, and his back is bleeding. Immediately thereafter, the back of Homer's shirt is completely intact.
Treehouse Of Horror XVI - S17-E4
Continuity mistake: At the end of "B.I.: Bartificial Intelligence," Homer climbs onto the ceiling and turns his head in a parody of "The Exorcist." He then lets go and lands on the bed. The only problem is that his body landing doesn't match the position it would from what we see on the ceiling. If he dropped down his face should be face down, body facing up and his head would be closer to the end of the bed. When he lands, his head is near the pillows, his body facing down and his head facing up.
Homer Badman - S6-E9
Revealing mistake: In the scene where Marge's coat pocket bursts open, the candy flows onto the floor. However if you look to the right of her some of the candy seems to almost float above the floor. The candy's direction is completely to the right but because of the floor being angled it spreads over one woman who is standing and there is nothing there to support the candy. (00:04:30)
Homer's Barbershop Quartet - S5-E1
Audio problem: In the scene where the Be Sharps first sing "Coney Island Babe" (I don't know what the song's really called) at Moe's, Skinner sings the rhythm. But when they sing the last few lines, you can still hear Skinner's part, but his mouth is moving like the rest of the group.
Treehouse of Horror XV - S16-E1
Continuity mistake: When Ned saves Moleman, we see where Ned is standing, there is no manhole beneath him yet when he catches Moleman there is one there. (00:02:30)
The President Wore Pearls - S15-E3
Continuity mistake: At the end of the episode Lisa gets on the school bus and in the back of the bus there is an emergency door with a small window in it. The following shot she starts singing out the back of the bus but the window has disappeared.
Homer's Triple Bypass - S4-E11
Continuity mistake: When Homer is eating the bacon and what looks like scrambled eggs after claiming Marge's oatmeal had a bug on it, the close up of the bacon shows that it is pink/purple and the eggs are yellow but the in the following shot, when Bart says, "Dad, there's a bug on that." the bacon and the eggs switch colours. (00:03:40)
Continuity mistake: When we first see union flag on fire, the flames are already consuming over the half of its upper edge. Then when we see it reflected in Hugh's eyes, no more than a half of the edge is burning.
Treehouse of Horror XIV - S15-E1
Continuity mistake: After Homer tries to stab himself with the banana, he drops it. But when Nelson's clothes disappear, the banana has vanished.
Marge vs. the Monorail - S4-E12
Plot hole: When Homer is trying to stop the Monorail, he grabs the big M from the side of the train and uses it as an anchor. However, when the M cuts through 'Springfield's Oldest Tree', there is no visible monorail track or supporting pole in the background.
Continuity mistake: In the first shot of Selma on the hospital bed, there's nothing behind Patty. However, when Marge starts to speak, we suddenly see two bags of drip mounted on a dripstand behind her. (00:01:55)
Continuity mistake: When Bart comes back into the classroom after the wolf attack, Ms Krabappel is writing on the black board and there is quite a bit of writing up there. After we see Bart the shot goes back to Ms Krabappel and all the writing has gone. (00:18:45)
Continuity mistake: When Homer goes to catch Maggie (after flying out of the car) he jumps over two cars in front of him and then falls over the second one and there is no sign of any cars in front of him. However in the shot before he climbs over the cars the aerial shot of Maggie flying in the air, all the cars on the bridge are bumper to bumper with no spaces in between them.
Continuity mistake: When Homer and Marge are entering the cinema, Marge is taking Maggie with her. But when watching the film, Maggie is nowhere to be seen.
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