When Hester takes the enigma machine out of the car and into her flat she does not take the box with the battery. The battery is not seen in subsequent shots. The battery was needed to use the machine.
When Hester and Tom Jericho are sat in the car in the barn kissing, the light reflected off Hester's glasses, show them to be modern coated lenses. Coated lenses would not have been around during the 1940's.
In the final scene, in London after the war (1946), Hester steps off the pavement and we see double yellow lines painted at the kerbside (denoting No Parking). These road markings were introduced much later.
During the train journey towards the end of the movie, the view from Jericho's compartment shows the train going in opposite directions before and after the stop at the station, despite the fact that the train is seen leaving the station in the same direction as it arrived.
the steam locomotive number plate in some earlier scenes reads 63601 which is the British railways number from 1948 onwards. later the first 6 is mysteriously removed leaving 3601 which is accurate for that period
When Admiral Trowbridge storms off to his car after tearing strips off Skynner, Logie and Jericho he gives a British army salute (palm facing the person being saluted) and not a British naval one (palm parallel to the ground) before entering his car.
Near the end of the film, when the submarine explodes, our hero is nearby in the water. Unfortunately, water transmits waves exceptionally well. Anyone in the water for at least a square mile would be immediately killed from the shock.