Factual error: In the scene where the king attempts to seize the five members from Parliament, Cromwell makes a dramatic refusal to leave and proposes various "Laws" to prevent his arrest. Cromwell was not one of the five members whom the King tried to arrest and no law can come into force until it had been signed by the reigning Monarch anyway.
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Suggested correction: It's more of a threat than a declaration.
Factual error: In the movie you see Scottish Pipe Band playing. Pipe Bands where not established in Scottish Regiments before the Crimean War (1854-1856), there were only solo pipers. (00:35:00)
Factual error: When the Japanese planes attack the airfield, none of the American planes have numbers or letters, just a star.