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.
Revealing mistake: The shot of Homer saying "Marge, when kids say bad these days, they mean good. And to shake your booty means to wiggle one's butt" is recycled from the opening scene from Life on the Fast Lane. Notice the animation is of a much lower standard than the rest of the episode.
Audio problem: In "Clown Without Pity" when Homer yells "The doll is trying to kill me, and the toaster's been laughing at me!" his mouth doesn't move.
Revealing mistake: When Homer takes out the dollar bill from his back pocket right before he puts it into the vending machine, the left side of the screen is cut off a little. You can tell especially with how the trash bin in the bottom left has a splotchy white line next to it.