Continuity mistake: When the Flanders and Simpsons first meet at the golf course, Flanders is wearing his usual long-sleeved green sweater over his shirt. After Homer says to him, "The fruit of my loins can beat the fruit of your loins any day of the week", the color of Flanders' sleeves is missing, making it look as if he's wearing a sleeveless pullover.
Continuity mistake: Bart is putting pool balls while training with Lisa, the 2 balls remaining on the table change from white to a pink/red. (00:14:20)
Continuity mistake: During the tournament, Abe Lincoln hole, there is only one hole to shoot for when his legs open up, after Todd hits his ball through, you see 3 holes from the backside. After Bart hits his ball the legs open up to reveal 3 holes to shoot for from the frontside. (00:19:25)
Continuity mistake: When Flanders' wife gives them the sandwiches in the recreation room there are 12 sandwiches, when Homer asks Ned to get him a beer there are only 6.
Continuity mistake: Flanders is seen signing the agreement with his right hand. In later episodes, he is known for being left-handed.
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