Continuity mistake: Springy the Olympic spring that Homer makes has 9 coils. Then we see the large version that has many coils, at the Olympics meeting. Homer's original spring is in his hand and now it has many coils also. When it cuts back to the stage, the large spring has few coils, like the very first time we saw Springy.
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.