Continuity mistake: In the scene in the airport bar, two pilots sitting next to each other have brown and gray hair, respectively. When they stand up, the hair has switched colours.
Continuity mistake: On the plane, where Marge is starting to act up due to her Fear of Flying, Homer and Marge's seat-belts have mysteriously disappeared.
Continuity mistake: When we first see Homer at Moe's at the beginning of the episode, he is sitting at the bar and there is an ashtray by his glass of beer. But after a quick cut to Moe, we return to Homer and the ashtray has disappeared.
Revealing mistake: When Moe grabs Ned Flanders' shirt at the bar, Ned's torso is incorrectly drawn over his arms as well as the mug he is holding. (00:10:50)
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious - S8-E13
Continuity mistake: When Bart is lying on his bed whipping cupcakes at the wall, there are already 2 on the wall but after he whips the 3rd, there are still only 2 cupcakes on the wall.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: When the janitor shows Marge and Homer into the Utility Room, the only equipment in there is a couple of mops. Later, the janitor comes back and pulls out a big vacuum cleaner that we never saw previously.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: At the retirement home, Grandpa pulls out some medicine from his cupboard. In the next shot, another medicine bottle that wasn't in the previous shots appears.
Grandpa vs. Sexual Inadequacy - S6-E10
Other mistake: When Grandpa throws the bottle to Homer, look at the bottle - at the angle it was thrown at, it should have missed Homer completely.
Continuity mistake: In the full view of Mr Burns' office when he is talking to Homer towards the end of the episode, there is only one fountain pen holder on the desk, but when Mr Burns tells Homer to leave after giving him his old job back, there are now two holders on the desk.
Continuity mistake: When Mr Burns tells Homer that he is only eighty-one in the meeting in his office towards the end of the episode, there is a fountain pen holder next to his arm on the desk, but when the camera is behind Mr Burns' chair in the next shot, the fountain pen holder has gone.
Continuity mistake: When Homer sobs after Bart dropped his bottle of Dimoxinil on the carpet in the bedroom, he drops the empty bottle next to the remains of the contents. When Homer is looking at Marge in the next shot, the bottle has disappeared.
Continuity mistake: After they say their goodbyes at the power plant, Karl asks Homer if he brought an umbrella and you can see that Homer is standing behind the doorway, but in the next shot he is now standing in the doorway.
Continuity mistake: When Homer opens the doors to the Executive Washroom, there is a sign on both doors, "Executive" on the left door and "Washroom" on the right door. When we see Homer walking with Karl and Smithers, the "Washroom" sign on the right door has gone.
Continuity mistake: When Homer runs out of the house with his new head of hair, there is only one doormat by The Front door. But in an overhead shot of Homer lying on The Front lawn surrounded by the children, a green doormat is now under the door.
Continuity mistake: When Homer parks his car outside Jake's Unisex Hair Palace, the doormat by The Front door entrance is light green but changes to dark green in the next shot.
Continuity mistake: When Homer is looking through the coat rack at the Royal Majesty, the coats he is looking through are coloured blue and red, but in the next shot they are now green and black.
Continuity mistake: When Homer runs out of the house with his new head of hair, there is a green mat on The Front doorstep. When the delivery man with the flowers is singing to Marge a little later on, the green mat is nowhere to be seen.
Continuity mistake: At the power plant's board meeting, look at Homer and you can see there is a piece of brown paper in front of him on the table, but when the camera is behind Mr. Burns, the paper in front of Homer disappears.
Continuity mistake: When Homer runs towards Moe's Tavern with his new head of hair, he looks into the window and you can see there is an empty beer bottle on the window sill next to him. When the camera changes to inside the Tavern in the next shot, the beer bottle has gone.
Continuity mistake: When the doctor (in disguise) gives Homer a wrapped-up present in the alleyway, they are standing next to a lorry and underneath the lorry there is some rubbish. But in an overview of the lorry in the next shot, the rubbish has disappeared.
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