Deliberate "mistake": The fossilised dog looks like the dog did when he was young; it should look old and decrepit, as the dog was when he died. (Presumably deliberate, to avoid a spoiler.).

Continuity: When Amy and Leela are wrestling, Amy's leotard changes several times. It varies between pink knee-length leggings and no leggings at all.

Continuity: The lava is close to the machine, until Fry runs to it, then it's a long way away.