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.]
Plot hole: Hooper says he can't poison Bruce because his skin is too thick and he'll have to go in the water and poke him in the mouth. However, when Brody stabs him in the head with the gaff, it leaves several bloody holes. It's just a bit too convenient for the plot to be believable that Hooper would choose to go into the water with a creature so powerful and dangerous (as opposed to at least trying to drug him from the surface first). And he had enough of the drug to try more than once: he fills one syringe from a good sized bottle of the stuff.
Add timeGrumpy Scot