Tree House of Horror VI - S7-E6
Continuity mistake: In "Attack of the 50 Foot Eyesores", the executive goes to the piano and you can see a penholder on his desk. But the camera angle changes to behind the piano in the next shot, the penholder has moved position and there are now more items on the desk.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Nightmare on Evergreen Terrace", when the teacher hands out the papers before the test, you can see that in the desk sitting next to Bart is a student wearing green sunglasses and has blue hair. In the next shot, Martin is suddenly beside Bart.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Nightmare on Evergreen Terrace", when Marge takes off her oven gloves you can see there is a plate beside her, but when she puts the gloves down in the next shot the plate has disappeared.
Much Apu About Nothing - S7-E23
Continuity mistake: During the party for Apu, Dr. Nick is first seen not wearing a coat, then he has his usual white coat, then he has a brown coat, and then the white coat again.
22 Short Films About Springfield - S7-E21
Revealing mistake: A black line briefly appears on Apu's forehead while he's tossing the tofu dog around.
Audio problem: When the car drives into the cornfield, Martin is heard screaming, even though he is still asleep.
Continuity mistake: In the overhead shot of Patty smoking, she is sitting on a greenish-gold car, the car then turns blue in the next shot.
Continuity mistake: When Homer gets up to make Mr. Burns' breakfast, Marge's nightgown is yellow, making her look naked, but in the next shot, her gown is purple.
Continuity mistake: At the funeral, while everyone is clapping for Bob Newhart, Mayor Quimby is seen with brown skin.
Scenes From a Class Struggle in Springfield - S7-E14
Audio problem: Homer's mouth is completely out of sync when he says "our savings?"
Team Homer - S7-E12
Revealing mistake: When the children are running down the hallway, the animation keeps repeating. Duplicates of the same children are running several times.
Continuity mistake: After Moe yells at Ralph, there's a woman in the background staring at Moe with an angry look on her face. She turns her head away from him after some seconds, but in the very next shot, she is looking at Moe with the same expression on her face.
Continuity mistake: When Milhouse snitches on Bart, Martin has grey hair and a black suit. In the very next shot he has his ordinary hair and is wearing a brown suit.
Continuity mistake: Jasper's beard is missing when everyone is singing "In-A-Gadda-Da-Vida" at church.
Who Shot Mr. Burns? (2) - S7-E1
Other mistake: As Chief Wiggum is being interviewed about the fugitive, his arm is shown to be in a cast due to the police van crashing at the Krusty Burger Drive-Thru earlier on. Yet when they get to the hospital, his arm is completely fine. (00:17:30 - 00:19:00)
Scenes From a Class Struggle in Springfield - S7-E14
Revealing mistake: When Lisa is first shown riding the horse, the horse's eye is colored solid red.
Continuity mistake: When Moe tries to convince Dr Hibbert that Moe's is a family restaurant, Carl's skin is yellow.
Continuity mistake: The X-rays of Homer's intestine change sides between shots when he is at the vet.
Audio problem: After being hit with the nuclear waste, Ranier Wolfcastle says "My eyes! The goggles do nothing" without moving his mouth.
Sideshow Bob's Last Gleaming - S7-E9
Continuity mistake: When Homer drives under the plane to save Bart from Sideshow Bob, you can see he drives under the plane twice.
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