Continuity mistake: When Moe is wiping the beer glass at the beginning of the episode, the glass is initially smooth but changes to dimpled in the very next shot.
Continuity mistake: When we first see Homer at Moe's at the beginning of the episode, he is sitting at the bar and there is an ashtray by his glass of beer. But after a quick cut to Moe, we return to Homer and the ashtray has disappeared.
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 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: 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.
Continuity mistake: When Patty and Selma bring food to the Simpsons' for one shot Patty's dress turns blue before turning purple again.
Continuity mistake: As Milhouse walks up to the TV to turn up the volume, Lewis is nowhere to be seen in a wide shot, but as Milhouse walks back over to the couch you can see Lewis sitting on the floor. (00:02:15)
Continuity mistake: When the family is talking at the dinner table about going to see Truckasaurus, the amount of food on everyone's plate continually changes between shots. (00:03:40 - 00:04:25)
Continuity mistake: When at the dinner table, Marge tells Homer and Bart that they can go to see Truck-o-saurus. In one shot Bart has his hands on the dinner table, but in the next shot his arms are by his side. (00:04:20)
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)
Continuity mistake: When Bart attempts to skate over Homer's car, his three mates are watching. Between shots they change from standing on the driveway to standing on the pavement. (00:10:55)
Continuity mistake: When Bart skates towards Homer's car, attempting to skate over it, the distance between the car and Bart changes between shots. (00:11:00)
Continuity mistake: When Bart falls off his skateboard after attempting to skate over Homer's car, as the shot zooms out you can see his board is nowhere to be seen. (00:11:05)
Continuity mistake: When Homer falls down the gorge, the medics lift him up on a bungee and to the top of the cliff. Between shots the edge of the cliff changes from green grass to brown rock. (00:20:05)
Continuity mistake: The guardrail at the Springfield Gorge keeps changing between shots when Bart is about to make his big jump; in the first wide shot there is a short rail opposite the "stone ramp." Then in the Bart-POV shot from atop the ramp, the rail is much longer, and the parking lot and picnic area behind it have disappeared. And when Homer is actually jumping the gorge, the rail disappears altogether.
Itchy and Scratchy and Marge - S2-E9
Continuity mistake: In the beginning after Maggie hit Homer on the head, it shows him laying on the couch with Bart & Lisa on the left. The next shot it shows the TV, in the next shot it shows Homer on the left sitting and Bart & Lisa on the right. It's impossible for Homer to get up and switch sides with Bart And Lisa in less than 5 seconds.
Bart Gets Hit By a Car - S2-E10
Continuity mistake: In Moe's Tavern, in the close-up of Marge as she says "Homer, look at me" the glass window behind her has a different pattern than in all the other shots (2 rows of red tiles instead of 3).
Bart Gets Hit By a Car - S2-E10
Continuity mistake: During Marge's testimony, Lionel Hutz has a neat stack of papers in front of him the whole time. But in the close-up when Homer and Hutz both cover their eyes in sorrow, Hutz has several pieces of crumbled paper and a broken pencil in front of him. The was not nearly enough time for him to make such a mess since the last shot of him.
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