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 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.