Plot hole: When Homer is seen at work in the flashbacks (before Maggie was born), he is at his usual control panel in sector 7-G, but he only began working here when Burns made him safety supervisor in season 1, "Homer's Odyssey". Before Maggie was born he should have been working at the conveyor belt with the carbon rods, where we saw him in the first couple of episodes.
Plot hole: In the scene where Bart has to choose the right Roman numeral door in order to avoid the tigers; right as the Shelbyville kids come bursting through the outer door, Bart picks the right door through humorous deduction and escapes. However, the Shelbyville kids are unable to open the door which doesn't make sense, since there is no lock on the door and there wasn't any mention of Bart blocking or sabotaging the door because only a few seconds later we see him on the street continuing to fret about the lemon tree.
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?