Best war movie mistakes of 1953
Factual error: When Lt. Dunbar is being interrogated in the Commandant's office you can see a map on the far wall. It is a map of Germany dictated by the Treaty of Versailles which ended World War I because it shows E. Prussia separated from Germany and does not include the annexation of Austria and Czechoslovakia. These annexations were completed before the start of World War II in '39 and certainly before late '44, early '45 when the film took place. It is highly unlikely any German officer would have this map displayed not only because it's inaccurate but because it displayed the territorial losses brought on by the humiliating defeat of World War I.
Factual error: If we are to assume that the British cruisers were Dido class with 5.25" guns, the assertion that the Essen would outrange them by 5000 yards is pretty much true. However, in order for the Brits to launch torpedoes, they would have had to close to inside of 20K yards, well within range of their main guns. Thus said, if the British cruisers were any of their 6 inch gun class, there would have been no advantage in range.