When Marge says, "I wish you wouldn't put Homer down like that.", Patty and Selma's dresses swap color between shots.
When Homer tilts his dinner chair backwards, cutting to a closer shot of him, he suddenly had a fork and knife he didn't have in the wide shot, a glass of white liquid that wasn't there, and the food in his plat changes their locations.
Wiggum pulled over the limousine with a unit that has a blue and red light on top, but in a shot where he's talking to Mel Brooks, the police car can be seen in the background with only two red lights.
When Homer drags Patty and Selma out of the dining room, all the kids have disappeared as well as their chairs and all the plates and glasses of white liquid except one. And the angle of Marge asking "What's that supposed to mean?" has the table laid out in a way that isn't possible without putting her on one of the ends.
When Homer is pushing random buttons at his work station in the nuclear power plant, there is a green panel with red circles, white circles, white squares, and a dial that disappears in a close up shot oh Homer talking.
When the IOU lands on the lamp it is projected onto the ceiling. However, if the message was written on normal paper, which is most likely, the projection would have just been a solid square rather than the message.
No one would've hired Homer to be a chauffeur if he didn't have a chauffeur's license.
When Homer and Lisa are watching the TV ad for the limo service, the panning shot provides an impossible perspective of the limo: Both the front and the back of the car face the camera, as if it were curved.
When chatting with Bart, Nelson's left pupil is in his right eye, and his right pupil is on his cheek.