Continuity mistake: As Bart is about to enter his house after trying to impress his friends by krumping, you can see he is entering the front door. However, in the next shot when he gets inside and Marge is waiting you can see that he has entered the family room, which is only accessible through the back door. Entering by the front door would place him by the stairs, at the front of the house.
Continuity mistake: When we see the overhead shot of Krusty crying at the Simpsons' table (just before he explains his story), we can see that Krusty has no meat on his plate. When we first see the family and Krusty after the story, there's meat on Krusty's plate. This is visible in the 'Homer's tuxedo' mistake picture.
Continuity mistake: When Mr. Burns falls onto the sundial, everybody starts gathering around. Marge is there, with Maggie. She left Maggie in the car and seeing as she went off to look for Homer, Bart, Lisa and Grandpa and that she was one of the first on the scene when Mr. Burns collaspses, it would be difficult to run back and get Maggie from the car.