Factual error: When the filmmakers were choosing existing warships to play the roles of the ships in the battle, they didn't quite match up some of the details. The Graf Spee is represented by USS Salem which has three triple gun turrets - yet in the Captain's cabin is a photograph of the real Graf Spee which had just two turrets. Likewise, HMS Ajax is represented by a Sheffield class cruiser with four triple gun turrets - yet in the fire control area there are just eight lights to indicate guns ready to fire.
Factual error: Towards the middle of the movie when when the British submarine leaves port with the Man Who Never Was onboard, it is flying what appears to be an American flag. The flag is visible for about ten seconds and if you look closely, you can see the field of blue of the stars and stripes in the upper corner.
Suggested correction: The flag, as can be seen before submarine sails and then from a distance, is obviously the White Ensign.