Dalby on his way to a meeting with Security Service is wearing a Trilby hat, after leaving the meeting with the Minister both are wearing Bowler hats.
An opening caption gives the date as "August 1963", yet a London mainstream cinema is still showing "The Manchurian Candidate", a film released about nine months earlier (and a box-office failure). The original novel was published in 1962.
Colchester Military Prison does not have Civilian Prison Officers controlling the prison, it has Military Provost Staff running it and controlling the prisoners.
When Jean is leaving Harry's flat in West Berlin, she enters a car with the licence plate DF-Q 25. While the format is correct, the DF part has never been used by a city or district, making the plate invalid.
When Palmer gets his case and is caught by Dalby, the door in the background has a German marking, "Für Personel". It should be "Nur für Personal".
Harry Palmer is wearing a beret with the Gloucesters badge but this regiment has a back badge worn on the back of the beret, which he doesn't have.
When characters are discussing the testing of Soviet atomic weapons, the black and white film footage playing in the background supposedly shows the dropping of a Soviet bomb. However, the aircraft shown is an American B-36, not a Soviet bomber aircraft.
There is a scene near the start of Episode 3 depicted as being a US airbase in England. The Hardened Aircraft Shelters (HAS) in plain view were built much later than the timescale of the story.