Factual error: The detective played by Rory Kinnear is shown in 1951 typing a request for Alan Turing's military records. He changes a name with correcting fluid - unknown in the UK in 1951.
Factual error: In the scenes at Kings Cross railway station in London, overhead wires are visible above the train; Kings Cross did not have these until 1975.
Factual error: When Denniston introduces Hugh Alexander he says he (Alexander) is a British chess champion. Alexander says "twice." This is not true. Hugh Alexander had only won the British chess championship once by 1940 (in 1938), his second win was in 1956.
Factual error: At the end of the film, the statement that the enigma code breaking was a secret for "over 50 years" is incorrect. The secret was only kept until the 1970s.
Factual error: The voice-over incorrectly describes the Post Box as a 'Trash or Garbage can', when an envelope is placed in the box, and later retrieved by someone using a key, towards the end of the film.
Factual error: The opening graphic establishes the year as 1951 when depicting the time Turing's home was robbed and he was arrested for indecency. The robbery and arrest actually occurred in 1952, and strangely enough the correct date is listed on the dispatch about the robbery handed to MI6 boss Menzies moments later. Even if one looks at the film as a work of fiction, the date on the on-screen prop is inconsistent with the on-screen graphic. (00:00:40 - 00:02:40)
Vader47000Factual error: There is no evidence that Turing was aware that Cairncross was passing Enigma decrypts to the Soviet Union.
Factual error: At the one of the movie they say "Turing's machine" inspired generations of scientists. "Today we call them computers" suggesting he invented the computer, which is wrong. Despite there being different opinions. The first computer was built around the beginning of the 20th century. It's very far fetched to claim he inspired the modern computer, if not bogus. (01:50:10)
Suggested correction: People debate about what constitutes a computer. For example, by some definitions a mouse trap should be considered a computer, and is far older than the beginning of the 20th century. But Turing created a system that modern computers were built upon and as a result is considered by many as the father of the modern computer. That you have a different view doesn't make it a factual mistake. The fact is this is an opinion, and many agree with what was said, so the statement cannot be considered an error. Just like the argument about whether Edison should be considered as the inventor of the light bulb (spoiler - light bulbs using filaments existed before Edison's experiments, but Edison created a PRACTICAL version).
Factual error: The railway carriages shown in a wartime scene are post-war British Railways Mark 1 carriages. Inside the train a compartment is labelled 'Standard Class' which did not exist at the time.