Though Turing's surviving niece Inagh Payne agreed that Benedict Cumberbatch's casting as Alan Turing was very well suited, she disagreed with Keira Knightley's casting as Joan Clarke stating that the real Joan was 'rather plain'
The 'bombe' machine 'Christopher' seen in the film, is based on a replica of Alan Turing's original machine, which is housed in the museum at Bletchley Park. Production designer Maria Djurkovic admitted, however, that it was made a little more cinematic by making it larger and having more of its inside mechanisms visible. It is neither a Turing Machine, which is the imaginary subject of his 1937 paper 'On Computable Numbers', nor a computer. The 'bombes' were not physically built by Turing, or at Bletchely Park. They ran at twenty 'clicks' per second, not the much slower rate in the film.
When Alan is at school in 1928, sitting with his friend Christopher, he has on his knee a paperback book of modern crossword puzzles. Neither paperback books nor modern crossword puzzles were common in 1928.
When Hugh and Alan sit down with the girls in the pub, Hugh makes a reference to "kicking someone's ass". This is both anachronistic and a geographical error as this phrase is widely regarded as American slang from later in the 20th century.
Detective Nock says that two professors became "radicalized" at Cambridge before they joined the communist party. But the term "radicalized" was not used in this way until the 1960s, when it was used in reference to civil rights groups.