Corrected entry: When Fry and Bender run into the head museum, they're greeted by Leonard Nimoy. Fry refers to him as Spock, which he chuckles to. Yet in a later episode (4-12 "Where No Fan Has Gone Before"), Nimoy denies the name Spock due to Star Trek being forbidden on Earth.
Corrected entry: When Fry is cryogenically frozen, alien ships destroy all of New York. Later in the episode, it shows most of the buildings in Old New York intact, only with the Empire State Building having fallen over and New New York being built on a platform above it. If all Old New York had been destroyed/built over, why was the cryogenics building intact and in New New York?
Corrected entry: This is the only episode in which Bender doesn't mention he drinks to power up his fuel cells, in fact he say "I can quit anytime I want" when Fry challenges him about it. Clearly the writers hadn't decided that this is why he drinks, as in later episodes he explains all the time.