Continuity mistake: In the very beginning of the episode, Bart places Santa's Little Helper's dish into the sink and begins playing with the faucets. Marge comes in, and the bowl magically disappears from the sink and it's missing for the rest of the scene.
Continuity mistake: When the person delievers the animation cell, his skin changes from white, to brown and then back to white. When bart looks through the letterbox to see who was there, his skin is white. When he gives the box to bart, it is brown. When he hits bart in the face and says "that's for keeping me waiting", it is white again.
Continuity mistake: At the very end of the episode, when Homer is being carried off by the crowd, you can see that the crowd carrying Homer, the people are small, so you'll have to look closely, but right before the credits, Marge's necklace changes from red to white, back to red and then finishes with white all in one shot.
Continuity mistake: When Bart is standing on the bench, Jimbo and Milhouse are standing in the front row, on the right side of the screen. But when there's the closeup (a second later), there are children shown in front of Jimbo and Milhouse and the girl with the purple hair is gone.