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 first attacks Michael, while he and a research assistant are on the dock, The shark proceeds to bite chunks out of the dock, ripping and tearing large pieces of wood with it's massive jaws. When the shark submerges under water, a large pool of red blood is seen, as if it has just killed a person. As there was no body in the water and the only thing attacked was the dock, there should be no blood.
On the beach before Ellen and Hoagie go off on their flight, Ellen is wearing a white sweater. On the plane she's seen wearing a green sweater (a light brown jacket over her shoulders); seconds later, as she grasps the wheel, her sleeves are blue! At the festival, walking with Hoagie, she's wearing that blue sweater. Several costume changes in the space of an hour or less, within the same story segment? Continuity, shame on you.
When the shark attacks the banana boat, The woman in front of Thea throws her arm around her when the shark is approaching. In the next shot, the shark is coming up out of the water and you can see the woman's hand is up in the air attempting to wrap her arm around Thea. She should have already had her arm around her like in the previous shot.
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.
It is stated repeatedly in the film, especially by Jake, that it is very rare to find a great white shark in warm water. In fact, great white sharks can be found in almost any temperature zone. What is rare is what has happened in 3 of the 4 "Jaws" movies, to have great white sharks in the cold waters of the American Northeast.
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.
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.
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.
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.
When the shark first attacks Michael in the Bahamas, Jake gets out of the water and climbs on top of the boat to scout for the shark. The yellow strap on his wet suit switches from the front to the back and to the front again.
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 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.