Continuity mistake: When Homer is walking upstairs after kicking Patty and Selma out for the second time, the wall that Homer was approaching is a darker colour than it usually is, and Homer walked up the stairs slowly. But a second later he closed a door, indicating that he went into a room. Are we really to believe that he could go very quickly from the stairs to a room in a matter of seconds?
Continuity mistake: When wedding has been just called off, Lunch Lady Doris calls everyone for wedding cake, and among people who rush to it we can see Moe (you can recognize him by his eyepatch), then, Lisa starts to walk off and among the people she passes by you can see both Lunch Lady Doris and Moe.
Revealing mistake: By the end, when fortune teller lays "The Fiance" card on the table, it instantly makes the same angle as other cards lying there, even though the teller's hand is still under it. It doesn't change the angle when she removes her hand from under it, as though it's floating in the mid-air all the time.
Continuity mistake: By the vending machine, Lisa first points her card at the cell on the right, then there's a zoom on the cells and we see her hand starting to point again, but this time at the cell in the middle. In the next shot, she lowers her hand with the card, which however in this shot is pointing at the cell on the right again.
Plot hole: When Bart locks Principal Skinner and Mrs Krabappel in Skinner's office, and tells them that they can't come out until they've reached an agreement, why didn't Skinner and Krabappel just climb out Skinner's office window instead of spending hours pounding on the door yelling to be let out?