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.
Revealing mistake: When Bart's dog is chewing on the TV remote, one of the shots on it is of "I Can't Believe They Invented It." with Troy McClure as the host. This is exactly the same shot from "Homer vs Lisa and the 8th Commandment". You can tell because Troy's voice is different. The lip sync is also out, revealing that the line "As an actor, my eyeballs need to look their whitest" is dubbed in.