Naval officers, in particular Rear Admiral Godfrey, would never wear a goatee beard. Since the modern age all British naval personnel would be permitted to wear a full set or nothing at all.
Some of the documents at Naval Intelligence are marked Top Secret. This term was not used until the United States entered the war so that the UK and US operated to a consistent system. Prior to 1942, the highest level of classification in the UK was "Most Secret".
Camp X is depicted as being in the mountains of western Canada, when in actuality it was located outside of Whitby Ontario, an area that is primarily flat farm land.
The US intelligence agency is mistakenly referred to as the CIA, when at the time that the show is set it was still called the OSS. The CIA wasn't created to take over OSS duties until 3 years later in 1946 which was after World War 2 ended.