Tree House of Horror V - S6-E6
Continuity mistake: In 'Nightmare Cafeteria,' when Lunchlady Doris spills food on Jimbo, it only goes onto him. In the next shot it is also all over the table. (00:16:15)
Revealing mistake: When Lisa is clapping erasers, you can see the alphabet above the board, and part of the A is cut off.
Bart Gets Hit By a Car - S2-E10
Other mistake: When Marge is being questioned, before she says 'If you don't have anything nice to say, then don't say anything at all', there is a shot over her shoulder looking at the blue haired lawyer. Not only is he (the lawyer) there directly in front of her, but he is also sitting on the bench with Burns. In all other shots his chair is empty as it should be.
A Streetcar Named Marge - S4-E2
Continuity mistake: As Marge is about to leave for her first audition, she walks across the room and she is wearing white slip-on shoes. Then her and Homer talk for a bit, then when it cuts to a wider shot after they talk, she now has her red flat-heels on. (00:03:30 - 00:04:00)
Deliberate mistake: The mouth on the panda costume is in a constant smile and at no point does Homer change it, even when he is in pain. However, when he is being pulled back under the curtain the mouth is open and the mask has a frightened expression. I suppose this was done on purpose, but it's still a continuity error of sorts.
Continuity mistake: When Homer is writing a note to Marge, he scribbles out Patty's name and writes his own name directly beneath it. When Marge reads it, Homer's name is under Patty's, but slightly to the right. (00:14:30)
Continuity mistake: When Homer calls the Fatherhood Institute about his poor test results, the guy is holding a cup with 'Super Dad' on it. In the next three shots the cup has jumped to being on his desk. (00:08:50)
Homer's Triple Bypass - S4-E11
Continuity mistake: When Dr Nick visits Homer for the first time, he leaves the door open. But later before the reporters come to the door, the door is closed. (00:13:40)
Continuity mistake: In one scene Bart is swinging on a washing line then we see Homer talk to Marge and he says "He'll soon get tired of it" then it goes back to Bart and he is facing the opposite direction and he is swinging on two washing lines. (00:04:22)
Team Homer - S7-E12
Continuity mistake: During the classroom scene where Bart reveals his Mad magazine shirt, he removes his sweater and puts it on his desk. In the next shot the sweater disappears. (00:03:40)
Radio Bart - S3-E13
Continuity mistake: In the scene where Bart tries to get his radio back from the well, watch the police barriers. When Lou and Eddie get coffee, they walk through one of the barriers, tearing it. Several shots later, this torn piece has vanished, and then the barriers disappear entirely. (00:15:40)
Continuity mistake: When Otto announces about Milhouse's party, 1, Martin is sitting two seats ahead of Bart and Milhouse, even though he was just talking to them, and 2, Sherri and Terri are nowhere to be seen. (00:01:35 - 00:02:35)
Continuity mistake: When Bart realizes he forgot his permission slip, the camera shows us that the paper is half-under his pillow. However, when he got out of his bed at the very beginning, the paper wasn't under his pillow. (00:01:00 - 00:03:05)
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.
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)
Homer Badman - S6-E9
Continuity mistake: When Homer mixes the Pop Rox with the soda he leaves the Pop Rox packaging over the can. After he throws the can and we see it in the air the Pop Rox packaging has disappeared.
Lisa on Ice - S6-E8
Other mistake: As Homer is signing Bart's academic alert form just before Marge starts talking to Lisa you can read the writing below the "Academic Alert" title, but the writing is completely incoherent including sentences such as "IMAEGTSIAD TSNHOJI NAMREB". Update; some of the "words" or parts of them are people's names, such as David, Stuart and Allison, but backwards. (00:03:50)
Radio Bart - S3-E13
Continuity mistake: When Rod and Todd talks to 'God' on the radio, the antenna keeps changing position for the entire scene. (00:08:50 - 00:09:40)
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