Factual error: Here's a big historical mistake. The character of German Admiral Lütjens is depicted overall in this film as a wild-eyed Nazi fanatic. In real life, he was distinctly anti-Nazi, vehemently protested the anti-Semitic actions of Hitler's regime, and was himself subject to intense Nazi scrutiny as he was a quarter Jewish and his wife was half Jewish. He was one of many German naval officers who fought only for their country, not Hitler.
Factual error: The battle of the Denmark Strait is wrong in that both sides are heading and shooting in the wrong direction. The Germans are shooting to starboard rather than port, and the British are shooting to port rather than starboard.
Factual error: The destroyer allegedly sunk by the Bismarck is named as the Solent. She would not have been much use in a 1941 torpedo attack, as she had no torpedoes and was not completed until 1944.
Factual error: The admiralty gets a priority message that two ships have been seen leaving the Baltic. The admiral and his chief of staff discuss "the Crete business", however the Bismarck sortied on 18 May, 1941, and the invasion of Crete happened two days later.
Factual error: The Director of Operations is handed a fuel state for KGV and Rodney, and is advised they are 140 miles astern of Bismarck. He asks if they steam at full speed can they catch her. Since Bismarck can steam at 30 knots, and the British ships at 28 and 23 knots respectively, it was a question that shouldn't have even been broached.
Factual error: Just prior to the sinking, men are scrambling on the burning deck, beneath a tall, fairly slim (and lonely) funnel that bears no resemblance to that of the Bismarck.