Continuity mistake: When Brody and Ellen are talking about Mike being seventeen and should have a summer job we see Brody placing his arm on the side of the door entrance. When it cuts to a close-up from behind Brody you can see he has lowered his arm so the camera can get a clean shot of Ellen's face. When it cuts he has his arm back up. (00:25:40)
Continuity mistake: When the teenagers are near Cable Junction on their wrecked boats, they see Chief Brody coming towards them on the Police Boat. We then see a close-up of Brody, and from his view he is approaching Cable Junction and the teenagers from front-on, with the teenagers on the right. When we see Brody approaching them as seen from Cable Junction, he approaches them from a completely different direction. He comes from behind them as if he approached from a different side of the island.
Continuity mistake: In the scene where Chief Brody comes home drunk, Deputy Hendricks comes over to express his sorrows. When he's leaving/already left, Both Ellen & Chief Brody comment on Hendricks as "Poor Jeff." In the first Jaws film, Brody calls him Lenny. Jeff is actually the first name of the actor who played Hendricks.
Continuity mistake: When Brody is with the photograph developer, who is developing the divers photos for him, he takes a photo from a box and puts it in a tray of liquid, and he then puts the lid of the box on properly. Then in following shots the box lid alternates from on properly, to off slightly. (00:49:00)
Visible crew/equipment: When Brody is rigging the winch it shows an underwater shot, presumably from the sharks point of view, if you look attached to the kids boat's there is a wire anchoring them down.