Though the film is set in 1943, contemporary cars can be seen in a couple of location shots in London: when Montagu and Admiral Cross come out from their meeting with the Joint Chiefs of Staff (1950s cars parked in the background); and again when O'Reilly is sitting on the park bench ('50s cars pass on the street behind).
The scene is where William Martin's father is saying good-bye to his body in the hospital and talking with Ewen Montagu. As the father leaves the room, the shadow of the mike is well in shot on the wall behind him.
While O'Reilly is waiting in his room to see if he'll be arrested, the light level outside varies continually over the hour of movie time. It starts in the evening. When O'Reilly looks out and sees the drunk it's already quite dark. But when the special branch officers arrive and hide outside, it's quite bright.
As the canister holding the corpse of "Major Martin" is winched out of the HMS Seraph, the last line of lettering on the side is seen to be mostly worn away and nearly illegible. In the very next scene as the canister is lifted onto the submarine's deck, the lettering is suddenly completely legible once more - "SPECIAL F.O.S. SHIPMENT".
When Lucy is sitting at the piano talking about Joe who O'Reilly mistakes for Wm Martin, she is holding a drink. The camera breaks to Pam and O'Reilly and when it returns to Lucy, she is no longer holding the glass.
In the scene where Montagu receives a telephone call from Gen. Nye summoning him to 10 Downing Street, there is a calendar in the background that reads Friday, April 12. In 1943, when this movie takes place, April 12 fell on a Monday.
When given a list of possible operation names to use, the name Operation Jubilee is listed as available. Operation Jubilee, in fact, was used the previous year by the Allies, in what is more commonly known as the Dieppe Raid.
When the Spanish fisherman finds the dead body on the beach it is supposed to be early in the morning. However, the sun is low in the sky over the water (i.e. in the west), indicating it's really in the late afternoon.