Factual error: When Brian fires a rifle at the shark from the boat, he fires the rifle multiple times very quickly. The rifle he is using is a bolt action rifle, which must have a bolt part moved before each fire. He does not touch the bolt.
Other mistake: In the last shot of the film, the zombies are walking across the bridge to New York City. Below, there are cars on both sides of the bridge driving to and from the island with absolutely no concern for the chaos that is supposedly taking place. I guess the filmmakers couldn't stop traffic for a few minutes to get the shot?
Factual error: In the last scene, the radio announcer in New York City states that the governor has declared a state of national emergency. Only the President can declare a national emergency, not a governor of a state.
Continuity mistake: During the underwater scene where the zombie is fighting with the shark, the zombie's arm is bitten off by the shark. However, we see him with the arm after he loses it, and without the arm before it is bitten off.
Continuity mistake: In the end scenes in the church, our heroes can be seen throwing bottles of kerosene at the zombies. The first one explodes into flames on the floor, but the following three bottles are all thrown into space where there is no fire. The fire has vanished.
Revealing mistake: When Dr. Menard is driving and discussing the zombie plague with the visitors, the "clean" part of the jeep's windshield (i.e. the path of the windshield wipers) appears to be cut out of the glass (probably to provide a better view of the actors and prevent the camera being reflected on the glass).
Continuity mistake: Paola Menard is in the village cottage alone, when the zombies begin to threaten her safety and attack. She then pulls the large wooden cabinet from the wall and pushes it against the door. However she pushes the dresser up against the door twice between shots.
Chosen answer: After the original zombie extra fell ill, the shark handler was made up to play the underwater zombie. The shark was tame, or at least enough to not attack the handler. The makeup would have been latex/oil based, so it would not have been affected by the water. I remember from the commentary that the filming took 1 or 2 days.