There is a basic skeleton of facts the movie gets correct: Alan Turing was homosexual; his work in mathematics and cryptography were instrumental in the development of the machines that cracked the Nazi code and led to modern computers; he was engaged to Joan Clark; his home was burglarized; he was convicted of indecency and sentenced to “chemical castration.”
Unfortunately, the movie includes a great deal of fiction: Alan Turing was open about his homosexuality; Joan Clark knew of his attraction to men; their engagement was not to rescue her from her conservative parents, they genuinely liked each other; he was not a brusque, humorless, narcissist; he did not singlehandedly design and build the machine; he did not name any of the machines he built “Christopher”; and he most certainly would not have committed treason to keep secret his proclivity that was not so secret.
The ultimate point of the film, on which the power of its propaganda rests, is that Alan Turing committed suicide because of the suffering he endured due to his sentence. While the determination that his death was a suicide is itself questionable, he died a full 14 months after his treatments, not while enduring them as the film depicts.
These inaccuracies and many more can be found at these articles at history vs hollywood, the guardian and slate. While I understand that film makers often add fictional aspects to historical events for powerful dramatic effect, i.e. Jack and Rose in "Titanic", I do wish they would take better care to get the historical data right. With a generation that gets it’s truth in 30 second bites, objective truth will be lost to slickly produced images and special effects.
Don’t take my word for it – read the articles, don’t trust the movie.
Have a little hope on me,