Continuity mistake: When the crew is in the submarine and they're just about to see the shark, Steve is holding on to the steering wheel. But when the view is of the steering wheel and little windows, no hands are on the wheel. Cut back to the crew, Steve is once again holding on to the wheel.
Continuity mistake: During the shoot out with the pirates on their secret island, Team Zissous' firearms change from Glocks 21's to Beretta 92FSs'. When the members are holding the guns without firing, they are in fact Glocks. Any scene where they are actually shooting, they are holding Berettas.
Continuity mistake: Warning: Spoiler. Following the shootout with pirates at the abandoned hotel, it is raining hard as Team Zissou makes their escape. When they arrive at the beach, it has suddenly stopped raining. There has not been a lapse of time, as the action on the beach is a continuation of the running sequence. Secondly, we see a young boy cooking something over a campfire. There is no way he could have built a fire in the heavy rain that was falling just a moment earlier.
Trivia: The character Steve Zissou, played by Bill Murray, is an homage to Captain Jacques-Yves Cousteau, who also wore a red wool cap identical to the caps worn by Zissou and his crew. Additionally, Captain Cousteau's ship was named Calypso, and in the film Zissou's ship is named Belafonte, a send-up because Harry Belafonte, a Jamaican American musician/actor, was referred to as the "King of Calypso."
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