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 Bart hands Ms.Krabbappel his final test, there are some shots going back and forth between their faces. During the first shot looking at Ms.Krabbappel, you can see a window behind her, and outside the window, there is no snow, even though there was a whole lot of it yesterday. During the next shot, the snow IS there. As the camera goes back and forth, the snow disappears and reappears.
Continuity mistake: When Homer is preparing the barbecue, he is wearing an apron that says "Mafia staff apron". After he goes to pick up the lighter fluid, it reads "Maffia staff apron", and after he has lit the barbecue, it is back to saying "Mafia".
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.