Sink the Bismarck!Goofs
The characterization of Admiral Gunther Lütjens in this movie is wildly inaccurate. He is shown as a zealot, a fanatic, denying reality until the end. In fact, Lütjens was a thoughtful, even morose figure - some survivors claimed that his tendency for fatalism damaged their morale. Absurdly, on screen the Admiral tells his men to "remember you are Nazis!" Lütjens was not a Nazi (very much the opposite, to the extent that he famously refused to perform the Nazi salute for Hitler before the Bismarck set sail), nor were the vast majority of his officers and crew.
In the film, Bismarck is attacked by British destroyers the night before she is shelled into a wreck by King George V and Rodney. Bismarck sinks one of the destroyers (the "Solent") after suffering torpedo damage. In the real battle, no British destroyers were sunk in this engagement and German sources indicate no torpedoes hit Bismarck during the destroyer attack.
In the "friendly fire" attack on HMS Sheffield, the appearance of the ship when she is spotted from altitude clearly resembles a battleship like the Bismarck rather that the long slim lines of a cruiser such as Sheffield. The same footage is used for the scene when the aircraft (correctly) Identify and attack the Bismarck.
Incorrectly regarded as goofs
When the aerial photographs are being developed, you can see the image appear when the print is in the tray of developer. The print is taken directly from the developer tray and the light is turned on only inches from the print. If this were done in reality, the print would immediately turn entirely black from the light unless the print had been transferred to a fixer bath first.
Swordfish torpedo bombers are shown taking off with slung torpedoes, and the torpedo propellers are spinning in the wind. The purpose of the nose propellers is to arm the torpedo. To avoid premature arming, the nose propellers would be wired to prevent spinning in the air. When the torpedo hits the water, the greater resistance would break off the wires and the torpedoes would then be armed after a few rotations.
About half way into the film the HMS Ark Royal and HMS Victorious are mentioned. Close ups of flight deck operations included a shot that showed the hull number R06. "R" is a NATO designation that was not utilized until after WWII. R06 is the hull number for HMS Centaur which was not launched until 1947.