Continuity mistake: The zipper of Burns' radiation suit disappears instantly when he's on the phone to the news station. (00:06:20)
Continuity mistake: When Burns hangs up the phone to Kent Brockman, his name tag on his radiation suit disappears. (00:10:20)
Revealing mistake: When Smithers makes Mr. Burns his Wine Spritzer, Burns makes Homer Employee of the Month. While Smithers is pouring the stuff in the bottle, his left hand turns black for three frames. (00:10:30)
Continuity mistake: When Mr. Burns tells Smithers that Homer is the next employee of the month, his huge red chair he was just sitting in has disappeared, and Mr. Burns is in a different position. (00:10:30)
Continuity mistake: When the salt spills on Milhouse's food, the table full of kids in the background has disappeared. (00:10:45)
Continuity mistake: When all the salt spills out onto Milhouse's lunch, the salt that was on his food tray has disappeared. (00:10:50)
Other mistake: When the family are having dinner and Homer has a beer, the can is grey instead of the usual red. This is rectified a few seconds later. (00:14:00)
Continuity mistake: When playing Monopoly the fold in the board is level with the P. Camera changes now the fold is before the O. (00:16:10)
Continuity mistake: Marge tells Bart not feed Maggie the Monopoly houses. Bart shows the box and says that there's enough of them. The shot later, the box has disappeared. (00:16:15)
Continuity mistake: Maggie spits a hotel out on to the board which disappears a few seconds later. (00:16:15)
Audio problem: After Barney falls over in his chair, you can hear him say, "Hmm, a pretzel." His mouth doesn't move. (00:21:15)
Like Father, Like Klown - S3-E6
Other mistake: When Krusty dials '1-909-SEX-CHAT,' he presses '90190' on the phone. (00:03:50)
Like Father, Like Klown - S3-E6
Continuity mistake: When Miss Pennycandy barges in on Krusty's 'Sex Chat,' she leaves the door open. It remains closed for the rest of the scene. (00:04:15)
Like Father, Like Klown - S3-E6
Continuity mistake: Lisa says about Krusty being Jewish and Homer's wine glass swaps side on the table. (00:06:20)
Like Father, Like Klown - S3-E6
Continuity mistake: When talking about Jewish people, Homer puts mashed potatoes on his plate that sometime disappear and reappear. (00:06:30)
Like Father, Like Klown - S3-E6
Continuity mistake: During dinner, Krusty does not have a shirt pocket until he pulls out his handkerchief. (00:06:45)
Like Father, Like Klown - S3-E6
Continuity mistake: Homer asks if Krusty is going to eat his meatloaf and is reaching across the table as he does so. The camera changes and he is no longer reaching. (00:06:50)
Like Father, Like Klown - S3-E6
Continuity mistake: Towards the end of the meal, Lisa has some meat left on her plate that disappears in some shots completely. (00:06:55)
Like Father, Like Klown - S3-E6
Continuity mistake: During Krusty's performance, the tables change from round to long and rectangular. (00:09:10 - 00:10:10)
Like Father, Like Klown - S3-E6
Continuity mistake: In Krusty's story after he has his makeup washed off by a rabbi, just after his father speaks to him his makeup suddenly reappears. (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