Much Apu About Nothing - S7-E23
Continuity mistake: When the mob leave Quimby's office, he had loads of things on his desk. When he pulls the picnic basket up, the desk is empty.
Continuity mistake: When the first photo is taken of Selma and Troy on their first date, Selma is wearing lipstick. When the photo is published, the photo shows her without lipstick.
Continuity mistake: Just before Marge tries to sell Skinner the tie rack, she is writing on something. She then puts her hands down by her waist, and then brings one up to turn it on and both up to pull the motor out. The point is that the pencil and the item she had in her hands have simply vanished, and we never saw her put them down either.
Tree House of Horror VI - S7-E6
Continuity mistake: When Professor Frink is explaining where Homer is, in "Homer3", Ned Flanders is leaning behind the couch between Bart and Marge, and Chief Wiggum is standing up. When Homer complains, Ned is between Marge and Chief Wiggum, who is now sitting down on the couch.
Tree House of Horror VI - S7-E6
Continuity mistake: For most of "Homer3", Marge's shoes are red. When Frink explains that Homer is 3rd Dimension, Chief Wiggum says, "Slow down, egghead". During this shot, Marge's shoes are green. When Homer complains, Marge's shoes are back to red. (00:18:05)
22 Short Films About Springfield - S7-E21
Continuity mistake: When Skinner and the superintendant are having lunch, Skinner brings in four burgers. The superintendant takes one, and suddenly there is only one left.
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer comes home with Apu, Lisa closes the book she's reading and slides it to the side on the sofa. When she stands in the next shot,the book has gone.
Continuity mistake: After Homer dodges the cannonball near the end of the episode, the blue platform that he stood on goes further away from the edge of the stage between shots, and when Homer hugs Marge the platform has disappeared and Peter Frampton's cooler has become closer to Homer.
Continuity mistake: When Homer is talking to Ned about having his own BBQ Ned is facing the fence but in the next shot he is facing alongside it with his head turned to Homer.
Continuity mistake: On Lisa's plate at dinner she has no mashed potato. During the lamb vision, her pork chops are now smaller and there's now mashed potato on her plate.
Continuity mistake: When Homer is on stage in Springfield and preparing to get hit by the cannonball, the speaker-tower, behind and slightly to the left of him, completely disappears in the wide shot right before Homer jumps off stage.
Raging Abe Simpson and His Grumbling Grandson in 'The Curse of the Flying Hellfish' - S7-E22
Continuity mistake: At Asa's funeral Burns and Grandpa both produce a key to unlock the compartment in the Hellfish monument, but even though they both take their keys out of the keyholes after turning them, all 9 keys are in place in the following shots.
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer,Barney and Moe are in Moe's making signs Moe says 'But they ain't bothered...' and leans on the pool table with his elbow.In the next shot he is leaning on it with his hand.
Continuity mistake: When Homer is stuck in the hole after saving the plant, Marge is seen in the background wearing lipstick. When Mr. Burns asks if there is anything he can do for them, there is a closeup of Marge and her lipstick is gone. When they cut back to Homer, Marge is again wearing lipstick.
Revealing mistake: When Lisa is explaining to the curator of the museum why she didn't tell the crowd of what she learned about Jebediah Springfield, if you look in the background none of the people on the far sidewalk are moving, almost frozen in place with some of them with their arms in the air yet everyone and everything in the parade keeps moving right along.
Continuity mistake: When George and Homer burst out of the manhole, there is a shot of the Simpsons' house covered in mud, then a quick one of it totally clean, then another when it's muddy again.
Raging Abe Simpson and His Grumbling Grandson in 'The Curse of the Flying Hellfish' - S7-E22
Continuity mistake: Grampa loses his red slipper as he is pulled by Mr. Burns' boat. Later it is back on his foot.
Much Apu About Nothing - S7-E23
Continuity mistake: When Barney is tranquilised, he falls with his mouth closed. In the following shots, it's open, closed, then open again.
Tree House of Horror VI - S7-E6
Factual error: In "Nightmare On Evergreen Terrace", Martin has a dream, in which he speaks Latin. At one point, he says a verb that doesn't exist: "morire". The words is "mori" (to die), "moritur" (noun dies) or "moreris" (you die). The "moirie" is also on the blackboard behind Martin. (00:08:20)
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer swings on the electric cable when attempting to get to his car, the cable has just appeared from nowhere because, the previous 'birds eye view' shot showed no cable.
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