Lisa's Pony - S3-E8
Audio problem: When Homer is crying after the tape is finished, what he says doesn't match his mouth. (00:07:25)
Continuity mistake: When the family are on the conveyer belt in the Knowledgeium, Homer turns round and grabs the handrail (after the Troy Maclure announcement) and his fingers are just touching the rail. In the next shot his hands are clasped to the rail.
The Boy Who Knew Too Much - S5-E20
Continuity mistake: When Homer and Bart see each other skipping work/school, Homer is eating a donut then drops it on the pavement when he sees Bart. In the next shot of both of them the donut has disappeared.
Homer Alone - S3-E15
Audio problem: When Marge is running errands, Homer gives her his bowling ball with a bottle cap stuck in a hole. She then takes it to Nicks. When he says, "Sorry lady, you've got the wrong Nicks," he shakes his head and makes an "Ohh" shape with his mouth, not saying anything. (00:03:50)
Continuity mistake: After Bart's career is dead, he is at his house, and Marge brings out a box of Bart related items. She pulls out a doll and hands it to Bart, as she is handing it to him, the doll's arms disappear, and then reappear when Bart touches it.
Continuity mistake: Ned's clothes are cut and torn in the huricane, but the next day, they are somehow clean and intact. He can't have gone home and changed, otherwise he would have seen everyone repairing his house.
Continuity mistake: When Homer's head gets caught in the middle of the draw bridge, a yellow stripe can be seen down the center of the bridge (where Homer has become stuck). However, in the closeup of Homer being hit by the cars, the stripe has disappeared.
Continuity mistake: When Chief Wiggum and Homer think that the convertible Ruth and Marge are in is a ghost car, they want to hold each other. In this shot, you can see 1 small star out of the backseat of the police car. But in the next shot, from the perspective of the backseat, there is a canyon top where the star would be.
Continuity mistake: When the two chinese guards are dragging Budda Homer along, in an overhead shot we see a desk, with one filing cabinet behind it. In the next shot, the guards stop to rest, and now there are two. (00:17:25)
The Ziff Who Came to Dinner - S15-E14
Continuity mistake: When the Simpsons first see Artie Ziff in the attic, as he stands up, there's a theremin behind him (corresponding with Homer's comment that the "ghost" was playing his theremin). Artie puts a sign up above it. However, when Artie moves to the rafters, the sign he put up is still there, but the theremin isn't.
Continuity mistake: When Patty and Selma bring food to the Simpsons' for one shot Patty's dress turns blue before turning purple again.
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: When the family are outside, in the shot just after Homer says "At the worst possible time" you can see the living room - everybody has disappeared in that shot.
Gump Roast - S13-E17
Deliberate mistake: Where do the "professional roasters" get those home movies of Homer's stupidity? No one could possibly have filmed his skiing mishap or the Funzo incident. Also, how does Maggie keep a mental record of celebrities that she didn't meet in person?
Last Exit to Springfield - S4-E17
Revealing mistake: When we see Lisa singing and playing the guitar for the second time, if you look to the right you can see a blue mark on the building that is behind her (On the middle turquoise stripe). It appears and disappears twice.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Nightmare Cafeteria,' Lisa and Bart run into the basement, to tell Marge they are cooking kids at school. Between shots Bart and Lisa swap places. (00:18:15)
Springfield Connection - S6-E23
Continuity mistake: When Marge is doing her grocery shopping, the boxes of caviar behind her change from green to red.
New Kids on the Blecch - S12-E14
Continuity mistake: When L.T.Smash sees his admiral, we see he his has badges on, yet when the shot changes and zooms in on him, they're gone, then they're back. (00:17:10)
Continuity mistake: At the thanksgiving dinner, Lisa tears one of the legs off of the tofu turkey, but in a later shot the leg is back on the turkey. (00:20:20)
Tree House of Horror VI - S7-E6
Continuity mistake: In 'A Nightmare on Evergreen Terrace', when the children are all discussing their dreams, Ralph's sling is blue. After the shot of Principal Skinner, Ralph's sling is white.
Continuity mistake: When the police talk about the bumper cars getting stolen by Jimbo Jones, you see him and his 2 friends riding off in bumper cars. From the side angle, there are 2 blue and 1 red car, but from the rear view, there is 1 blue, l red, and 1 green car.
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