Nick Holden tells Matt Sherman that the boys up in Las Vegas would say he is trying to make his point the hard way. Sherman latter repeats this to someone else. In 1941, while it existed and had gambling, Las Vegas was not yet the gambling and entertainment center it is known for. It was a small dusty town that was mostly a rest stop on the way to Southern California. People might know of it, and specially navy servicemen might know of it since they would stop there on their way to Pacific, but it wouldn't have been a standard cultural reference as it would be in the 1950's and beyond.
In 1941, Reno, NV would have been a more appropriate reference as it was better known as a place to gamble and vacation.
When Lt. Holden tells the Marine guard about the "blackout regulations," he says the order came from Adm. Nimitz. If this is set in mid-December 1941, Adm. Nimitz wasn't commander-in-chief, yet. He took command on 31 December 1941.
The map on the wall of the office where Cary Grant and his superior are discussing the damages the submarine suffered during the Japanese raid at the beginning of the movie is clearly a mid '50s world map. The borders of European countries are clearly post war and the same about India and Pakistan that didn't exist as countries on 1941.
When Lt. Commander Sherman is talking to Captain Henderson the mention the submarine tender Bushnell as being in Darwin, Australia, that is not correct, the Bushnell had been transferred to duty as a Hydrographic Survey ship and renamed Sumner AGS-32 in 1940. The closest submarine tender was actually USS Canopus AS-9, which was in the Cavite Naval Yard.
When initially leaving the dock, the ship's chief engineer told the captain they only had 1 of the 4 engines available. Yet when they pulled out he gave the order "all ahead 1/3rd, starboard 1/3rd". This would take two different engines on two different props.
During an air raid, several bombs go off near a truck Tony Curtis is driving. A cloud of smoke is shown coming up vertically at the driver's door while the background scene shows the truck is moving at a high speed. The wind created by the truck's forward motion should have blown the smoke horizontally.