Children of a Lesser Clod - S12-E20
Continuity mistake: When Ned Flanders is asking Homer whether or not he is running a daycare centre, there is a radio behind him. The aerial on it changes position in subsequent shots.
New Kids on the Blecch - S12-E14
Continuity mistake: When Homer is pinching Lisa with the "jealousy bug", the sign behind him changes from a gift store to an antique store.
Continuity mistake: When Homer sits down in the movie theater, all the rows are completely full, including the row behind him. When he turns around to talk to Selma, the seats directly behind him are empty. Then, when Homer turns back to the screen, the Sea Captain and Dr. Hibbert appear sitting directly behind him.
Continuity mistake: In the very beginning of the episode, Bart places Santa's Little Helper's dish into the sink and begins playing with the faucets. Marge comes in, and the bowl magically disappears from the sink, and it's missing for the rest of the scene.
I'm Goin' to Praiseland - S12-E19
Continuity mistake: When Flanders' girlfriend pulls up at the end, from one angle she's wearing a pink shirt with what looks like a white vest over top. But from another angle her shirt is all white.
Continuity mistake: When Homer sees the hotdog that Duffman holds up near the end of the episode, the order of the condiments on the hotdog change in subsequent shots.
Children of a Lesser Clod - S12-E20
Continuity mistake: When Bart and Lisa are trying to win back Homer's affection they are sitting on the top of the stairs and push the skateboard with the present on it down the stairs. In the next shot it rolls into Homer's legs yet it would be impossible as he was standing in the main living room which is to the right of the stairs. Pushing the present down the stairs it would go straight into The Front door.
Continuity mistake: When Homer, Lenny and Carl are in the cafeteria, and Homer is drinking beer, his chair changes from being blue, to red, then back to blue again, between different shots. (00:06:45 - 00:07:15)
Skinner's Sense of Snow - S12-E8
Continuity mistake: When the hamster Nibbles has rolled back to Skinner, it takes the lid of the ball off, and the lid lands on the ground. When the hamster is rolling away from Skinner it doesn't put the lid back on, it just leaves it on the ground, but in the next shot the lid is suddenly gone.
Continuity mistake: When they are riding the boat type raft, the stripes change from red on the left and black on the right, to the other way around and then back again.
Continuity mistake: Before Homer sees his vision of Caesar Romero the day sign next to him says 9. After the Duff executives see him talking to nobody they decide to take him away and when they get down there the sign now says 12 with the president of Duff confirming it in his speech. Doubtful it took them 3 days to get down to him and not much reason for Homer to take 3 days off the sign seeing as he was almost passing out from the lack of food.
Continuity mistake: When Marge is putting Lisa and Bart's clothes on, she puts Lisa's dress on Bart and Bart's shorts and t-shirt on Lisa, but 2 seconds later, when they are entering the kitchen, they are wearing their normal clothes.
The Great Money Caper - S12-E7
Continuity mistake: When they are driving home Marge starts to moan at the children to quiet down. In this shot she has no lipstick. In the next shot from outside the car she has lipstick on and has it for the rest of the scene.
Skinner's Sense of Snow - S12-E8
Continuity mistake: When the children are sleeping in the canteen at school, Bart is resting his head on a red sweater. In the close up of him and Lisa, the sweater has now turned dark green. It's not because of the dark that we see it like that because there is a bit of light at the beginning of the next shot and we see the jumper to be dark green.
New Kids on the Blecch - S12-E14
Continuity mistake: When Bart and the group are singing at school, when we see L.T.Smash, his arms are down then instantly in the next shot, they're on his sides. (00:08:10)
Continuity mistake: When Krusty is telling his daughter that he lost her violin, keep an eye on the door of the appartment. A grey bar appears and disappears on the door underneath the "eyeglass" between shots.
Continuity mistake: There are two problems with Lisa's Indian burns. When we first see them, she has 4 burns. Then, while she is showing them to the bullies, there are 3, then 4 again. Then, in the very next scene when she is walking with Nelson in the schoolyard, they are gone altogether.
Continuity mistake: Bart's magazine appears in the second shot of him and Lisa talking, it's not in the first.
Continuity mistake: Milhouse is seen in the school bus during the Lisa segment, even though he was with Bart at the time.
Tree House of Horror XI - S12-E1
Continuity mistake: In Reaper madness, there's a scene which Homer wakes up being the grim reaper, he puts the robe on at which point he is wearing a singlet. In the next scene where God turns Homer back to his regular self he is wearing his white shirt.
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