Factual error: When Hooper sees the hole in the hull of Ben Gardner's boat, he uses his knife to pry out the shark tooth. The tooth is located at the bottom of the hole, with its flat root side stuck deep in the wood and its pointy side facing up. It is completely impossible for the shark's tooth to become wedged in the wood this way, while he takes a nice bite out of the wood hull.
Factual error: When the shark is attacking Quint, the boat etc., his eyes do not roll back. Great White sharks roll their eyes back when they attack. Sharks that don't roll their eyes back have protective eyelids, but the shark doesn't close its eyes either.
Factual error: In the scene when Brody and his deputy, Hendricks, are at the boat dock watching all the fishermen get into their boats, there are many shots when you see the town behind them. If you'll notice, there are no leaves on any of the trees, suggesting that it may be autumn. The events in the movie are supposed to occur during the 4th of July holiday. This mistake is also repeated when the mother of the boy comes to the dock and slaps Brody.
Factual error: Chief Brody is wearing his badge on the wrong side of his chest in every scene. That must have been deliberate for reasons only known to cast and/or crew. A sworn Peace Officer always wears his badge on the left side of his chest, symbolizing that it is over his heart.
Factual error: When Hooper examines the remains of the swimmer he lifts up what is left of the woman's left hand and forearm. The blood and flesh are a bright colour. Blood and flesh discolour very quickly on a dead body - these bits should be a lot darker and the flesh a lot paler and dark bluish in colour.