When the police car flies off the cliff, there is no badge on the door.
When Bart and Homer are discussing the babysitter, they are in the family room, during Bart's closeup, he's standing next to the TV - a room away.
During the closing monologue, the Narrator states that Homer was sent to Fort Meade, Maryland to be subject to chemical experiments. Fort Meade is a military intelligence base. Chemical and biological experiments are conducted at Fort Derrick, Maryland.
When Ruth Powers first appears to ask for a power sander, she rings the doorbell from the backyard. Not only does she ring the doorbell from the backyard, which wouldn't have a doorbell, but she's in the backyard in the first place.
Homer's mouth is closed throughout his line "Ah, young love."
Despite his arms being trapped in the vending machines, Homer somehow manages to call Marge and tell her about the mishap.