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: Some of the gun crews (usually skulking behind the guns) on the "Graf Spee" are wearing their American helmets. (U.S. Navy refused permission for German helmets to be worn, but regardless of the reason it is still a movie mistake.)