Homer Badman - S6-E9
Character mistake: When Grandpa is putting up the American flag for Homer's public access show and Marge says the flag only has 49 stars, there are actually only 38: 8+7+8+7+8.
Homer Badman - S6-E9
Continuity mistake: When Homer's badly-edited "Rock Bottom" interview is shown on TV, the hands on the clock behind him keep jumping around between all the different cuts. But when we saw him giving the actual interview earlier, the clock behind him stayed at 5 o'clock the whole time. The hands on the clock are also slightly different.
Homer Badman - S6-E9
Continuity mistake: Homers car gets blown over by a helicopter, and gets dented, and all the windows smash. But in the next overhead shot the car is parked on the side of the road, perfectly intact.
Homer Badman - S6-E9
Audio problem: When Bart and Lisa hug the T.V and Homer asks them if they are, they respond with "No". However, Lisa's mouth moves but you hear no sound.
Homer Badman - S6-E9
Continuity mistake: Just after Marge's left jacket pocket bursts open at the candy convention the shot changes to a shot of Marge's face. The next shot her right pocket has suddenly burst as well and the candy in it is no where to be seen.
Homer Badman - S6-E9
Continuity mistake: When one of the pockets of Marge's coat explodes (when Homer is stealing the rare Gummi), a huge pile of candy comes pouring out. When she bends down to pick some up, there isn't nearly as much candy there as before. There are people picking up the candy with her, but they would have to pick it up extremely fast, and they aren't.
Homer Badman - S6-E9
Continuity mistake: When Homer mixes the Pop Rox with the soda he leaves the Pop Rox packaging over the can. After he throws the can and we see it in the air the Pop Rox packaging has disappeared.
Homer Badman - S6-E9
Continuity mistake: After Marge's left pocket rips in the candy convention, she goes to start picking up the candy when we see that the right pocket has ripped all of a sudden. When Homer and Marge start running away the pockets are no longer ripped and full of candy again.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: Homer leaves the Simpson house to go to the farm house in the station wagon, and when he parks in front of the farm house he's driving his pink car.
Grandpa vs. Sexual Inadequacy - S6-E10
Other mistake: Look closely when the clerk scans the books. Ueberroth is a brown book, and Al Gore's book is green. The book that sends the message to Al Gore is the Ueberroth book.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: While hiding the fact they are looking at sex books from Bart and Lisa, Homer picks a green book. When we see what he's reading, it's a grey "Maple Thorpe" book.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: On the book on conspiracy theories that Bart buys, there's a picture on the back of the author. The picture changes several times throughout the episode.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: When Homer and Grandpa are trying to sell the tonic at the mall, when Homer is trying to sell tonic to the Critical Man, all the tonic bottles on the table are actually empty. In the next shot, they're full.
Grandpa vs. Sexual Inadequacy - S6-E10
Revealing mistake: When Doctor Hibbert drinks the bottle of tonic, the amount of tonic never actually changes even though it should have gone down a considerable bit.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: When Lisa jumps off the tyre swing, her dress is fairly dirty. When Homer drives off, the bottom is dirtier than before.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: At the old Simpson home, Grandpa and Homer run into each other and collide on the porch. In this shot, the windows are dark, but in the next, all the windows are instantly lit up by the fire, which would not be possible in the given time.
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.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: In one scene in Bart's treehouse, Wendell's skin is yellow, rather than its usual white color.
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