Continuity mistake: After Krusty is done doing the special promotion commercial, he is given a telegram informing him of the Soviet boycott. However, this is a flashback, and at this point in time Krusty is illiterate (as will later be established in season 1) so he shouldn't be able to read the telegram.
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: When Homer and Bart are watching a clip of Sideshow Mel on wowee sauce and Bart then says "I'd give anything to go to that show", he has nothing in his hand. The shot cuts to Homer and he then says "I'd sell my first born son" and then the shot cuts back to Bart. When the shot cuts back to Bart, a Buzz cola can has appeared in his hand out of nowhere. (00:08:20)Casual Person