Marge tells Grampa that she found his cigar box dug up in the back yard. However, in Part 1, we clearly see the cigar box and hole in the front yard.
During the concluding episode, when Lisa is explaining to her mother how Homer's prints could have gotten on the weapon, a flashback scene shows Homer drop reaching under his car seat to get something he dropped; he touches various items, including the gun, then right AFTER the gun, he touches the lollipop. Yet at the end of the episode where Mr. Burns recounts, in another flashback, when he was accidently shot by Maggie, he gun and lollipop fall under the seat, but the lollipop falls to the LEFT of the gun.
In Part One, the retirement castle falls into a sinkhole (meaning Grampa has to live with the Simpsons) but in Part 2, Chief Wiggum visits Jasper in the retirement castle to ask about his leg.
When Jasper's car hits the crashed paddy wagon, Homer jumps down next to the wagon, which is being pushed forward. Yet in the very next shot he is shown running ahead of the wagon.
Kent Brockman claims that "dozens of people are gunned down every day" in Springfield. However, Wiggum asks why no one would report another shooting when Smithers recalls shooting Jasper Beardsley.
The bullet that Mr. Burns was supposedly shot with is actually an unfired bullet - the shell is still attached.
The police never question barney Gumbel even though was a prime suspect.
When Groundskeeper Willie claims he got arthritis in his fingers, from space invaders in 1977. Wiggum assumes Willie is talking about the arcade game. However, Space Invaders was not released until 1978. (Edited as a character error because Wiggum assumed Willie was talking about the game. Willie appeared to believe actual space invaders are the reason behind the handicap.)