Plot hole: When Hooper and Chief Brody are trying to get the Mayor to re-close the beach after finding Ben Gardner's boat, they fail to mention they also found Ben Gardner's severed head. The Mayor would be forced to re-close the beach if yet another confirmed shark fatality had been mentioned, but Hooper and Brody never bring that important detail up. [This is still a mistake, but the explanation for this is that the scene where they find Ben Gardner's head was not in the original script. Originally, they just found his boat. Spielberg felt the scene needed a little more shock value so they shot the part with the head in a swimming pool long after the main filming had been completed.] (00:50:20)
Suggested correction: First off, it wasn't a severed head as you can still see the body attached to it, and second, what difference would that make? Two people and a dog already died, with the death of the Kitner boy being witnessed by several people, and the beaches still stayed open because the mayor was too stupid to close them. Not only that, but during the scene you mentioned, I believe it was Hooper who said that THREE incidents had occurred BEFORE the third killing takes place on-screen.
And not only that, but the mayor witnessed Hooper saying that the shark they caught was not the same one, or at least it was possible that it wasn't. Either way, shark attacks were happening, but the mayor did nothing about it.