Continuity mistake: When Roger Meyers throws his nameplate at the writer the second time, the animation is repeated from when he threw it at him earlier. It's more obvious because his mouth doesn't match what he's saying and the background is orange instead of purple like the rest of the scene.
Continuity mistake: Millhouse is in the classroom at the beginning when Principal Skinner says that superintendent Chalmers is coming for a surprise inspection, but when they show Nelson he is getting crud put down his shirt. How could he be at two places at once?
Continuity mistake: When Marge comes to pay for her shopping, she empties her left pocket on her coat, but when Sanjay finds it in her pocket, it's in her left pocket. We know it wasn't in her pocket anyway because when Sanjay finds it, it is bigger than the size of her pocket.