Continuity mistake: When Lisa is watching tapes of Francine's bullying, there is a scene where they are at the pool. Francine is wearing nose clips in this scene. But when Lisa freeze-frames and leans in to closer inspect the shot, Francine's face is shown on the screen without nose clips. They appear again when Lisa exclaims "Of course. The nose clips."
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.
Deliberate mistake: When Bart and Edna are watching "Holes" in the IMAX theater, Edna sighs and pulls out a locket which we can see the back of. After opening it up to reveal pictures of her and Seymour, we find out its actually a triptych when she opens up another image of Seymour's mother. From the way she unfolds this extra picture, Seymour's mother would have had to be facing outwards, but in the previous shot the back of the locket was blank.
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.
Continuity mistake: On the trip back from the gardens, Homer rear ends the car in front of him on the bridge which sends Maggie flying out of the car. In a long shot of the bridge whilst Maggie is in the air you can see the car has changed to an orange color instead of the usual light purple color. The two cars in front of them also change during shot. The one in front of the simpsons changes from a normal red mid sized car to a blue van, whilst the car in front of that one changes from being a green car to a blue one during the aerial shot of Maggie.