The ax in Itchy's hands disappears when Homer places him in the hamster cage.
Homer receives a hair transplant from Snake after the latter is executed in the electric chair, which then causes Homer to be possessed with the spirit of Snake. The problem is, before a prisoner is executed in the electric chair, the prisoner's head is shaved, in order to facilitate direct contact between the electrode and the head. (Not that The Simpsons should be expected to be too accurate on matters like this.)
After Snake is executed in "Hell Toupee", someone makes a remark about how they will now "chop him up for organs." Organs from prisoners executed in the electric chair cannot be used in transplants; the electrocution pretty much fries them to a crisp.
When Bart decides to use the plutonium rod as a battery (factual mistake in itself), Lisa cautions him against hammering it into the TV remote control, saying that it is "highly unstable!" Bart then manages to fit it in without apparent incident. In reality, unstable elements have a high rate of radioactive decay; it does not mean that they are explosive.