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: 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: When Homer tells Carl and Lenny about the movie they watched, they change positions, and there is much more on the table. (00:03:35)
Revealing mistake: If you look carefully in Mr. Burns' surveillance cameras, the workers are identical. (00:02:50)
Continuity mistake: When Otto announces about Milhouse's party, 1, Martin is sitting two seats ahead of Bart and Milhouse, even though he was just talking to them, and 2, Sherri and Terri are nowhere to be seen. (00:01:35 - 00:02:35)
Continuity mistake: At the beginning, when we see the exterior shot of the bus, it is full of kids. In the interior shots, 1) before the twins talk to Bart and Milhouse, every seat is empty, even Sherri and Terri's. 2) when the bus arrives at the school, we AGAIN see a full busload of kids. (00:01:30 - 00:02:25)
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)
Continuity mistake: There are many mistakes when Homer is checking for donut flavors, i.e. the positions of the donuts, the topping, etc. (00:03:50)
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: The card Bart has written for Milhouse is blank inside. However when Lisa looks at the card, the pun of the joke (on The Front of the card) is now there. (00:01:15)
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: The zipper of Burns' radiation suit disappears instantly when he's on the phone to the news station. (00:06:20)
Continuity mistake: Milhouse unwraps his present from Bart and the wrapping paper stays under the box. When he's seen a few seconds later however the paper has gone. (00:01:50)
Continuity mistake: When Bart is writing the card for Milhouse, he is writing on the right hand side of the card. This changes to the left hand side in the close up. (00:01:10)
Continuity mistake: Maggie spits a hotel out on to the board which disappears a few seconds later. (00:16:15)
Continuity mistake: When Burns hangs up the phone to Kent Brockman, his name tag on his radiation suit disappears. (00:10:20)
Continuity mistake: When the purple jam pops on the core temperature dial, it leaves some residue on the dial which has disappeared in the very next shot. (00:05:10)
Continuity mistake: When Homer is talking to Lenny and Carl about the movie his pink doughnut disappears from his hand. (00:03:45)
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