Continuity mistake: After the "car chase" the white car gets put in the barn. When the black car arrives it is covered in mud (so much they have to wipe it off the windscreen) from the dirt track. The white car only has a few specks of dirt.
Continuity mistake: In the scenes in Bletchley (south of England) it is obviously early Spring (daffodils, few leaves on trees), but towards the end of the film, and apparently only a few days later, when a German U boat surfaces off the coast of Scotland, it is clearly high summer, with all the trees covered in leaves. Trees don't come into leaf that quickly, and the seasons are always later in Scotland.
Continuity mistake: In the scene in Scotland where Puck is rendezvousing with the German submarine whilst being watched by the British security services and police, there are several shots of the sub through binoculars supposedly from the perspective of the British on top of a hill. These views are all (with the exception of the last one of Puck meeting the sub) from sea level.