The British submarine that releases the corpse of "Major Martin" is completely dry immediately after it surfaces from the ocean depths.
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 taken to the submarine HMS Seraph, the last line written on it is entirely legible. Then 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."
In the beginning of the film, the body of "William Martin" is shown washing up onto a Spanish beach while a small sailboat sits just offshore. But when the body is again shown washing onto shore later in the movie, the sea is empty.
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.
When the body is delivered to the submarine the naval party on the dock is called to attention by "Shun!" In the Royal Navy this is "Ho!"
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.
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.
Near the end,whilst discussing the matter with Special Branch in the pub, the time is around 10:45 pm. Pubs were closed around 9:30 during the war, although there may have been a special licence for 10:30 pm, but never as late as 10:45 pm.
"Pam" was the name given to Martin's supposed girlfriend and not a staff member at MI6, as was depicted in the movie.
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.
As the canister containing the body is lowered to the submarine, the officers discuss with the sub Captain what his cover story is for the crew concerning the canister's contents. The next shot of the group is wider and shows them accompanied by at least half a dozen other ratings, all within earshot of their conversation.
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).
When Lucy is stamping books at the library, the sound occurs just slightly before the stamp connects with each book.
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.
When waiting to see if the unknown spy O'Reilly will turn up for the trap (at the place to see if he gives himself away by asking about the fictitious Martin), some of those waiting wear their military and police uniforms etc. Although men in such dress would've been very common during the war of course, a German spy would hardly turn up to ask suspicious questions if spotting them waiting there even if not knowing why they were there.