The "Admiral Graf Spee" is, quite obviously, a Des Moines class American heavy cruiser of the post-war period, the USS Salem. The actual "Graf Spee" had six main guns instead of nine, three each in one forward and one aft gun turret. She was also a much smaller and lighter ship.
The American reporter asks the telephone switchboard operator to get "NBC, CBC, ABC" on the line. Although NBC and CBC (Canadian Broadcasting Corporation) existed in 1939, when this movie was supposed to take place, ABC wasn't formed until 1943.
After HMS Cumberland had joined Ajax and Achilles replacing Exeter, the three ships portrayed in following scenes were still the same three initial cruisers, with HMS Jamaica playing a role of HMS Exeter.
As HMS Exeter prepares for battle the personnel on the bridge are looking to the port bow; however, when the ship is shown immediately afterwards, all of the weapons are pointing over the starboard bow.
When the crew of the Ajax cheers the Achilles in long shot, the crew (including both bridges) are wearing dark blue naval uniforms, but when it switches to close ups of both bridges, they are in tropical white uniforms.
When the petty officer runs forward on Exeter after she is hit in the bow, he reacts to the explosion of another shell before the hit occurs. He then completely disappears between frames and a repair party suddenly appears. It can also be seen that the ship is not moving through the water during these scenes.
When Graf Speed refuels from Altmark, Bernard Lee's character goes on deck to observe. He is no longer on board the ship playing Graf Speed (USS Salem). The secondary and anti aircraft armament is now of an Allied Light Cruiser (2 pdr pom Poms and twin 4 inch DP mounts).
When Captain Dove is first brought aboard the Graf Spee, the anti-aircraft gunners are wearing US-pattern steel helmets, not the German "coal-scuttle" Stahlhelm. This is noticeable in various other scenes as well, and is due to the fact that the Graf Spee is being played by the USS Salem.
A symbolic scene, when a crane lowers a lifeboat with Captain Dove into an aircraft hangar of "Admiral Graf Spee", and the roof closes over it, could not happen, because such hangars were typical for US ships only, and "Graf Spee" had no aircraft hangar.