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.
Continuity mistake: When Homer realises that the bear was only agressive because of the electrical tag, they share a bear hug. The back of Homer's shirt is torn to tatters, and his back is bleeding. Immediately thereafter, the back of Homer's shirt is completely intact.
Continuity mistake: At the end of "B.I.: Bartificial Intelligence," Homer climbs onto the ceiling and turns his head in a parody of "The Exorcist." He then lets go and lands on the bed. The only problem is that his body landing doesn't match the position it would from what we see on the ceiling. If he dropped down his face should be face down, body facing up and his head would be closer to the end of the bed. When he lands, his head is near the pillows, his body facing down and his head facing up.
Revealing mistake: In the scene where Marge's coat pocket bursts open, the candy flows onto the floor. However if you look to the right of her some of the candy seems to almost float above the floor. The candy's direction is completely to the right but because of the floor being angled it spreads over one woman who is standing and there is nothing there to support the candy.
Audio problem: In the scene where the Be Sharps first sing "Coney Island Babe" (I don't know what the song's really called) at Moe's, Skinner sings the rhythm. But when they sing the last few lines, you can still hear Skinner's part, but his mouth is moving like the rest of the group.