The film creates the false impression that the Chain Home system was not proven to work until the eve of the Battle of Britain - 9th July 1940. In reality, the first five CH stations had been fully tested and declared operational in August 1938. Chain Home was continually expanded as part of the Dowding System right up to the start of the Battle of Britain. Also, Watson-Watt was not dismissed as depicted in the film, he continued to play an important part in the development of radar throughout the war.
The aircraft in the initial test is of the right era but the wrong type - it looks like a de Havilland Rapide, while it should be a Handley Page Heyford, something in which the film makers had little choice, since not a single example of a Heyford survives, flying or not.
The term 'Mole' was coined by John Le Carre in his novel 'Tinker, Tailor, Soldier, Spy' in 1974.
The label megahertz (MHz) was not used as a measure of radio frequency until the late 1960s. Prior to that the term used was megacycles.
Whilst wiring the first machine the wire colours in the mains cable are brown and blue. At the time, these would have been red (live) and black (neutral).
Early in the film, in a scene set in 1935, a British Air Ministry official is looking at photos of Luftwaffe aircraft. Photos of a Heinkel 111, Junkers 87 Stuka and Messerschmitt 109 are shown. Prototypes of these planes were flying in 1935 but the photos depict much later versions of the aircraft. For example the Stuka is a Junkers 87-G version with under-wing cannons which didn't appear till 1943.