As Brody argues with Mayor Vaughan about keeping the beaches closed over the Fourth of July, he states that five people were chewed up in the surf (in New Jersey) in five days, in 1916.
In fact, it took place over a twelve-day period, and three of the victims were attacked in a tidal creek.
(An Eagle Scout like Steven Spielberg should have known that.) When Hooper first meets Quint, Quint asks him to tie a sheep shank. However, the knot Hooper ties is actually a trumpet knot, not a sheep shank.
They both serve the same purpose (shortening a length or rope) but they are tied differently and have a slight difference in appearance.
The two sharks mentioned by Hooper during Chrissy Watkins's post-mortem are Carcharhinus longimanus, the Oceanic whitetip shark, which is a pelagic shark and doesn't enter the surf zone where the Watkins character was killed, and Isurus paucus (not "glaucus"), the Longfin mako, and is also not known for coming as close to shore as depicted in the movie.
Its bite would never be mistaken for a great white's.
Isurus Glaucus is a Short Fin Mako, and is only found in the Pacific Ocean, not the Atlantic, as the Isurus Oxyrinchus would be.
Sheriff Brody learns from his deputy that the boy scouts are doing their "Mile Swim" in the bay for their merit badge.
While the Boy Scouts of America do offer a "Mile Swim" patch for those scouts able to swim, non-stop for that distance, there is no merit badge that requires swimming a mile.
As the shark passes the Orca and Chief Brody fires his gun at it, the second gun shot can be seen hitting the water before the gun fires it.
It happens immediately following the cut after the first gunshot.
Right after Brody empties his gun on the shark as it swims past the boat, you see a surprised Quint come towards the stern alongside Hooper and you hear his dialogue "I can't believe it.
Two barrels and he's going down again." But Quint doesn't move his mouth at all.