Continuity mistake: When Marge is racing the school bus, as the bus jumps out of the ditch you can see that the bottom of the bus is painted to resemble a skateboard. When the bus lands from this jump, however, the bottom of the bus is an even grey colour.
Springfield Connection - S6-E23
Continuity mistake: Before Marge sees Homer parking violation, if you look at where he is parked over the first handicapped spot there is a car parked in the first non-handicapped spot. A bit before Marge arrests him there is now a non-handicapped spot between the car and Homer's car. (00:14:35 - 00:15:05)
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.
Continuity mistake: When the burglar points the gun at Apu and says "Hand over all your money in a paper bag" Apu immediately replies "Yes, yes, I will". But when Bart sees this incident on TV later, the time between the burglar demanding the money and Apu replying "Yes, yes" is much longer.
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: After the clown balloon that rips at the car dealership there is a bit of material left over and there is also a cord attached to the wooden platform where the balloon was. After a reaction shot, it cuts back and the material and the cord have both disappeared.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: Carla's "Carla" ring is only on her finger in the closeup.
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: When Homer makes the food with the mix of Tom Collins mix, cloves and a pie crust you can see the labels on the Tom Collins mix and the cloves change between mixing the ingredients and after tasting them. Also the top on the Cloves bottle keeps changing through the scene. When Homer takes the bottle out of the fridge you can see a red top on it. When he sits down the top has disappeared and starts pouring the cloves. When the shot changes the red top is back and it disappears after that. (00:15:20)
Radio Bart - S3-E13
Audio problem: Just after Krusty kicks Sideshow Mel into the big birthday cake on his show, he says "Hey kids" but his mouth doesn't move right.
Continuity mistake: When Lisa decides to take Miss Hoover's Teacher's Edition, we see "Teacher's Edition" on the spine of the book. But when Lisa puts it in her bag the spine of the book is completely blank.
Audio problem: When we see Steve Sax driving, he says "What a nice little town" but his lips don't move.
Revealing mistake: When Moe and Barney are seen drinking wine at the wedding, somebody walks away with a tray. When they are drinking the animation is repeated because you can see part of the tray keeps coming on and off-screen. (Look by the bottom right). (00:13:25)
Continuity mistake: In this episode Hans Moleman's skin colour is yellow. However in "Duffless " his skin colour is brown and in other episodes it is a dark yellow-green colour.
Home Away From Homer - S16-E20
Continuity mistake: Ned's front door before he and his family leaves opens on the left side (when looking at it from outside), but after the "Coach" has moved in, it opens on the opposite side.
Marge vs. the Monorail - S4-E12
Audio problem: When Mr Lanley is playing the piano, he plays some chords with both hands. During the line "Put up your hands and raise your voice", he plays the same chords, but at a different note, with only one hand.
Continuity mistake: When Nelson asks Bart what song he is playing as they wait for the bus, Nelson's vest is orange and his shirt is bluish. However, when the bus arrives and Nelson goes to get on the bus his vest is now bluish and his shirt orange. (00:10:10)
Continuity mistake: In the scene where Homer is going down the escalator, in the Costington's Centre, after he gets on two men follow him, then a woman, yet when the shot changes, it's a man then a woman then the other man. (00:00:45)
Factual error: The tongue Lisa sleeps on in the museum isn't anatomically correct. It shows the bitter and sweet taste buds as being side by side on the surface of the tongue. In reality, different taste buds are not in specific places on the tongue. I wouldn't normally complain, but this is supposed to be in a museum.
Continuity mistake: Near the start when Marge is putting jam on bread, she spreads it on the last piece but as she puts it on the plate it changes to a blob in the middle.
Continuity mistake: When Homer is driving to Truckasaurus there is a wide shot of the road with two cars on it, but in the next side shot of the road, the road has loads more cars on it. (00:06:30)
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