Character mistake: At the beginning, Sheriff Brody walks onto the "boat" that takes people and, at most, two cars across the water to the mainland. A car joins Brody with 3 men, the medical examiner, the major and the newspaper man. Brody has been told, by the medical examiner, that it was a shark attack that killed the young woman who swam at night (the first death in the film) but now he is being coerced into saying it was a boating accident. Meanwhile, the man who handles the "boat" has already put it in reverse, heading back where they have come from Nonetheless, the mayor says, "You can take us back now." Turning around, he would have seen the folly in his words.
Continuity mistake: When the guy is standing on the beach in the opening scenes the sunset is covered by cloud. When seeing the sunset from the woman in the sea's perspective the sky is clear with no clouds.
Continuity mistake: When Jaws gets trapped between the cage and the boat the shark is really thrashing about. Cut to the surface and Brody is trying to free the cage - the surface of the water does not match the actions of the shark.
Revealing mistake: On the second day aboard the Orca, Quint fires a barrel into the shark and they start to pursue it. There are some overhead shots of Quint on the pulpit and during some of these shots, you can see some sort of tow cable. It's visible on the bottom of the screen between some of the supports of the pulpit.