Continuity mistake: At the end of the film the fleet were instructed to sail towards the burning vessel, which would have meant that they were travelling west - into the setting sun. Given the location of Montevideo on the River Plate it is somewhat dubious that the sun would set over the sea even at that time of year.
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.