Plot hole: When the castle is about to blast off, Brad and Janet abandon Dr. Scott's wheelchair at the door of the castle and carry/drag him across the porch and down the steps. After the blast off, Brad, Janet, and Dr. Scott are on the grass and have been blown some distance apart from each other (in the UK version, there's another song where Brad and Janet crawl toward Dr. Scott so they are blown farther apart than shown in the US version). It seems extremely unlikely that the remains of Dr. Scott's wheelchair just happened to fly from the doorway to land directly under him during the blast. Brad and Janet can barely crawl so they didn't move him or it. (01:34:10)
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.
Plot hole: When Vic steals the food from the group in the desert, we see he's been standing about 100 yards from them, all the while they've been digging. This is filmed on the Bonneville Salt Flats, with completely flat ground for miles around. Did the group just not notice a guy (and a dog) standing that close to them? Did they not think of protecting their site with a guard (there are 2 kids and a cripple there, but even they don't notice Vic until he's just ten yards away, running towards them)? As well, the crime 'boss' character allows Vic to get away and does not chase him - he even laughs that someone has the guts to try it. Food is very precious in this world, and nobody would likely allow this theft, much less a criminal boss. (00:15:45)