Michael Caine's plane crashes in the ocean, but when he climbs aboard the Brodys' boat, his clothes are dry. Caine explained that they waited so long for the camera to turn over that his shirt and pants dried in the sun.
Near the end of the movie, the shark makes its presence known to Ellen by lifting itself out of the water so its head is over the ledge of the ship. In the next shot, part of the boat is missing. About a minute and a half after the shark eats the shocker, it reappears behind the undamaged boat.
When they spot Ellen from the plane, the shark is still a long distance from the boat. A moment later it is at the boat and jumps out of the water. The shark couldn't have swum that distance in such a short time.
When the shark pursues Michael through the shipwreck, what appears to be an enormous meaty tongue flicks in and out of the shark's mouth as it tries to bite him. Great Whites have an organ called a basihyal, which is very similar to a tongue, but it is stuck to the base of the mouth and cannot move as depicted in the film.
Hoagie refers to "the shark that killed Martin and Sean", although Martin wasn't killed by a shark, but by a heart attack. However, Ellen had been insisting that his heart attack was from fear of the shark, so he was likely speaking figuratively.
A shark just killed a young girl on the beach, but only Mrs. Brody goes out looking for it. In reality, the entire island population would be out in their boats, chumming the waters and fishing for sharks.
When the shark attacks Michael Brody and forces him out of the submarine, an underbelly shot of the shark eating the sub shows a large, rectangular hole in its stomach. It's only visible in the theatrical release and the UK television version.
Jake is twice seen working on the shocker device with a screwdriver. The first time he is ineffectually twisting the screwdriver backwards and forwards. The second time it clearly isn't engaging with anything.
When the shark leaps out of the water, as Jake is about to apply his electric gadget, the shark suddenly has a third pectoral fin on his chest area, pointing down between the other two. This is obviously a disguised support bracket to lift the shark as high as possible.
The goof items below may give away important plot points.
Mike is standing when he shocks the shark. Just before the beast is impaled, Mike he is sitting without the shocker. In the next shot, he stands with the shocker and delivers another jolt. It's only visible in the theatrical version.