As the film announces at the start, it based on a true story. The essentials are true, and to get so much history into a film things have to be condensed. Unfortunately unnecessarily inaccurate things were portrayed which didn't save any time. For example, Turing mutters under his breath so most audiences will not notice, that the Poles made the first crucial breakthrough. By the start of the war, the Poles led by Marian Rejewski had been breaking Enigma for over six years and built the first machine, called a "bomba" in 1938.
In July 1939 the Poles passed on all the information to the French and British including details of the bomba and their successes at a meeting which included Denniston. The problem started to mount for the Poles and later the British when other rotors could be swapped in and the indicator method was changed by the Germans. The film is correct in showing that Turing's genius was using known words from the coded messages to reduce the myriad of possibilities. This idea happened in 1939 and so he started from the outset to design the British "bombes" to use this method, not after they had been running for months.
Four senior code-breakers, not just Alan Turing, but also Gordon Welchman, Stuart Milner-Barry and Hugh Alexander wrote to Churchill in 1941 over Denniston's head about the shortage of staff and praising Edward Travis. In February 1942, Denniston was demoted and transferred elsewhere. His successor, Edward Travis, transformed the procedures.
Cairncross, played by Downton's ex-chauffeur, never appeared at Bletchley until 1942 and the alleged blackmail is an unnecessary red-herring.
The idea that there would be a chart on the wall in Hut 8 showing the latest positions of all Atlantic convoys is laughable. This chart was in a secure bunker in Liverpool that was as closely guarded as Bletchley Park.
Turing's team had no input into how the information was to be used, but it is true that Ultra intelligence had to be supported by other information and so patrols were sent out to find what was known to be already there.
Lastly Turing would never, ever, have disclosed even the existence of Bletchley Park to a detective he had just met.
The performance of Benedict Comberbatch is exceptional, and the rest of the cast good. Keira Knightley is pretty enough to have turned even Turing, but, despite the lines that told us, she never gave the impression she had a double first in mathematics from Cambridge.
Good film, though it could have be closer to reality without making it longer or more complex.