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.
Continuity mistake: The Bismarck is sighted by a British agent in southern Norway, sailing out of the Baltic into the North Sea - east to west. But the view through the agent's binoculars shows the ship sailing from right to left on the screen - which would be sailing west to east from the point of view of an observer on the Norwegian coast.