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.
When asked what the Enigma machine does, Jericho explains that "it turns plain text messages into gobbledygook." The word "gobbledygook" was invented by U.S. Republican Maury Maverick on March 30, 1944 (imitating the sound of a turkey) while the film is set in 1943.
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.
Although set during the Second World War, all the scenes in and around Trafalgar Square show modern London buses in the background. At the end of the film, at least one RT bus had visible route number boxes on the roof - the first batch of RT buses had this, with drop cabs, and were introduced before the war.
The railway coaches seen in the film are British Railways Mk1 stock, which were not introduced until 1951; the train should have been in LMS Maroon Livery - grubby in wartime. The final coach had a BR Eastern region running number, i.e with the prefix "E".
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.
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.
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 - based on the BR number it would be a LNER (ex GCR) class O4 built 1911.
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.
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.
When the U-Boat sights the convoy at night, the crew on the bridge deck are wearing red goggles. The red goggles were actually worn inside the U-boat so the regular lights would not affect the bridge crew's night vision. The goggles were taken off once they got on the bridge deck.