Continuity mistake: The man conducting the tour of the box factory tells the children that they will not be able to see a finished box, as the boxes are assembled in a separate location. However, moments earlier we saw a flat box going through a machine, and coming out finished.
Continuity mistake: When Homer is shouting at Skinner about losing Bart, if you look closely you can see that the box with the red cap goes past Homer. However, when he turns round and sees that red cap on a box, that box has already gone by.
Continuity mistake: After Bart's career is dead, he is at his house, and Marge brings out a box of Bart related items. She pulls out a doll and hands it to Bart, as she is handing it to him, the doll's arms disappear, and then reappear when Bart touches it.
Continuity mistake: When Bart is writing from the books in the kitchen, he is seen writing on the paper. In the next shot of him, the paper is clean.
