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.
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.
Continuity mistake: When Marge comes out of the kitchen at the beginning of the episode, there are three ice cream sundaes on the tray she is holding. When Homer says "Hitler!", we cut back to Marge and there is now only one sundae on the tray.
Continuity mistake: During the dinner scene at the beginning of the episode, Homer is eating a chicken leg. When Bart says "Hitler", we cut back to Homer and the chicken leg he was holding has disappeared.
Continuity mistake: When Homer says "Miracle breakthrough?" when watching the commercial on the TV, he is holding a spoon in his right hand. In the next shot, the spoon disappears.
Continuity mistake: When Homer is watching TV at the beginning of the episode, Marge takes away his plate of leftovers and puts an ice-cream sundae in front of him on his tray. When we see him a few shots later, his plate is now back on the tray with the ice-cream sundae on top of it.
Continuity mistake: When Homer is gazing at the commercial on the television, Bart is beside him but there is no sign of Lisa. After a quick cut to the TV set, we return to Homer and Lisa is back again.
Continuity mistake: When the doctor brings the "Hair in a Drum" product from under his desk, you can see in front of Homer there is a bottle of Dimoxinil and two gravity boots. When we see a close of the product in the next shot, the bottle and gravity boots on the desk have disappeared.
Continuity mistake: When the doctor places the items that come with the Dimoxinil on his desk, he places the scalp massager next to the pad. When Homer asks the doctor how much, we cut back to the doctor and the scalp massager is now on the pad.
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