Continuity mistake: When Mr. Burns pushes the child on the swings, he somehow manages to defy the laws of physics. When he pushes the child forward for the last time, he swings forward, then back, hitting Mr. Burns in the head. He then swings forward again, hitting Mr. Burns from behind. Mr Burns starts saying "You've won this round..." and the child then hits Mr. Burns from behind again. In order for this to happen, he would have to go completely around between the second and third hits and you clearly see he doesn't.
Continuity mistake: Before Marge sees Homer parking violation, if you look at where he is parked over the first handicapped spot there is a car parked in the first non-handicapped spot. A bit before Marge arrests him there is now a non-handicapped spot between the car and Homer's car. (00:14:35 - 00:15:05)Lummie
Continuity mistake: After Marge's left pocket rips in the candy convention, she goes to start picking up the candy when we see that the right pocket has ripped all of a sudden. When Homer and Marge start running away the pockets are no longer ripped and full of candy again.Lummie
Other mistake: As Homer is signing Bart's academic alert form just before Marge starts talking to Lisa you can read the writing below the "Academic Alert" title, but the writing is completely incoherent including sentences such as "IMAEGTSIAD TSNHOJI NAMREB". Update; some of the "words" or parts of them are people's names, such as David, Stuart and Allison, but backwards. (00:03:50)Lummie