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.
Continuity mistake: When Alistair Hennessey is lamenting with Steve Zissou about pirates aboard the Operation Hennessy vessel, there is a shot of Alistair lounging on a yellow sofa. To the left of the shot there is an opened silver laptop, but when the camera quickly cuts back to this shot, the laptop is in a semi-closed position. (01:04:45)