$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Revealing mistake: At the dinner table Homer says something like "as you know it's always been my lifelong ambition to be a blackjack dealer." During this line, for some reason they appear to have used a clip from an older episode (Season 3 / Episode 3 - When Flanders Failed) and dubbed the line over. For one thing, the animation is of a much lower standard than the rest of the episode. And perhaps even more telling, when he says it, he is holding a fork with some food on it, but from the earlier shots we know there is no food in front of him.
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: When Marge comes home after the bogeyman incident, Homer trips over a footrest. You can see Bart sitting there however his pyjama's are a dark green color when before they were a bright green color. (00:16:35)
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: As Marge arrives home and sees the bullet holes in the door, the shot changes to a POV shot from behind the door and you can see there are some changes in the holes. The first change is there are three bullet holes on the right hand side which are all the same distance from each other, when she enters the middle hole has moved closer to the bottom one. The other change is the large hole in the middle of the door. On the bottom right hand side its shape goes from being a little irregular to a more round shape. (00:16:20)
$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)
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: As Bart is on the phone trying to book his new act, you can see there is a split down his white shirt. When the shot changes and he tells Lisa to be quiet you can see that split has disappeared. (00:15:05)
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: When Marge enters the bedroom, the family appears from behind the mattress, and Maggie's outfit is her traditional blue, but when Marge picks her up her outfit is white. (00:17:10)
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