Audio problem: When Bender wins the Poker Tournament, Leo Wong says "Two kings and with three kings on the board, that give Bender five kings", his mouth doesn't match what he is saying at the end of the sentence. (00:21:00)
Continuity mistake: When Leo, Fry, Leela and Amy look at Leo's golf ball in the golf course through the telescope, you can see there is one free telescope. When Leo walks off to put the golf ball in the hole, the free telescope is still there. When Leo leaves in his hover car, the free telescope is gone. (00:25:25)
Factual error: Leo says he smells potato, but he is in a space suit and in space, making it impossible for him to smell it. (00:33:00)
Continuity mistake: When Leela covers Leo with a fence, Frida Waterfall is behind her. Moments later Frida is back at the Honeybun Hideout. (00:50:10)
Continuity mistake: When Professor Farnsworth says "Money talks" he holds up a dollar. In the next shot it is in Hermes' hand. Then in the next shot it is back in the Professor's hand. (01:13:15)
Character mistake: When everyone starts counting down to blow up the Violet Dwarf, everyone starts at 10 downwards. Yet 40 seconds later, they are still counting down. (01:19:40)
Suggested correction: Its very common for movies and TV shows to do this. Just because they say 10 seconds doesn't they can't spend more time going through the thoughts in Fry's head.
Continuity mistake: When the Planet Express ship bursts into the explosion ceremony Bender is wearing a Feministas mask. When the No.9 Man talks to the encyclopod he is no longer wearing it, it reappears when the encyclopod flies off and Zapp Brannigan tries to arrest them. (01:25:00)
Continuity mistake: Fry, Leela and Amy's clothes change as soon as they get on the Planet Express ship at the end. (01:25:40)
Audio problem: When everyone is saying "Go" whilst going into the black hole, Fry and Leela continue saying "Go" after they have closed their mouth. (01:26:50)
Deliberate mistake: When Bender wins the poker tournament with five kings, Leo Wong holds up five fingers (on one hand). But all the characters in Futurama only have four fingers on each hand. (Confirmed on DVD commentary).
Other mistake: In the crowd near the end, if you look very closely you can see unit 2013 twice.
Audio problem: At the end when they are flying towards the black hole and they all say "Go, go, go", the shot cuts to Fry and Leela. They continue to say "Go". But when they close there mouth, they continue saying "Go" even though they just closed there mouth.
Continuity mistake: After Leo blows up the Eco-Feminists, one of them lands on Fry and he is knocked out. Then when Leela says the Muck Leech may not be cuddly, Fry is awake as if he regained conciousness. But then minutes later Fry is still knocked out.