Just after Pike sends Anna outside to act hysterical, he looks at her through the window; however, she momentarily appears behind him, inside, while he is meant to be looking outside at her.
When the car drops Pike off at his London headquarters at the beginning of the film, a streetlight across the street is lit. No streetlights were lighted in London during World War II in order to prevent bombers from using their light as guides to their target.
When Anna shows Jeff her Auschwitz tattoo, she doesn't say anything about what it is. Jeff looks hurt and asks her "Which one?". She says first Auschwitz then Revensbruk. Until the US military invaded Europe, the concentrations camps were not well known. Until the liberation of the camps, the numbers tattooed on prisoners arms were not known of, so Jeff would have no reason to recognize the tattoo or ask "which one".
The Allies would never have been so reckless as to send into Portugal or any other neutral country any person who had specific knowledge of the pending D-Day landing for fear that person might be captured and tortured into revealing what he of she knew. Read "The Deceivers: Allied Military Deception in the Second World", the comprehensive and exhaustively-detailed book by Thaddeus Holt.
There would not have been any SS in the war room of the OKW, only Heer (Army) personnel, except for possible liaison officers from the Kriegsmarine, Luftwaffe and, only doubtfully, Wafen SS who would not have had any input into troop dispositions.
The phony newspaper which Pike is given on arrival in hospital, has a front page item about the UN. Although the United Nations first opened in 1945, the name comes from January 1942, when Franklin D. Roosevelt issued a proclamation outlining the basic set-up and goals for such an organization. This is all that the Nazis would have needed to make this phony report.
A sign in the fake American forces hospital reads "physiotherapy". This is the British term for what Americans call "physical therapy". Major Pike is used to the British and Americans working together closely, as shown in the opening scenes, and would not be suspicious about this status quo continuing into the near future, especially as the cover personas of Walter Gerber and other hospital personnel seem to be British.
Around 1:50: the "barbed wire" is completely smooth and can even be seen twitching when disturbed, revealing it to be common twine.
Early in the film, a woman furtively searches Major Pike's rooms. She examines two letters addressed to him. The stamps on the envelopes are from the U.S. "Liberty series", first issued in 1954: 2-cent Thomas Jefferson and 3-cent Statue of Liberty.
The radio introduces the song "Mairzy Doats" as an "oldie," a term first applied to songs in the 1959 LP series "Oldies But Goodies", an anthology of 1950s rock 'n' roll hits that were no longer on the Pop charts.
As with many World War II films made in the 1950s and 1960s, the makers were careless with women's clothes and hairstyles. The women in the Lisbon restaurant were wearing 1950s dresses, and Eva Marie Saint's hairstyle is definitely 1960s.
Anna wearing supposed wedding ring on right hand. Later in film older lady was wearing ring on left when awoken in the middle of the night. Europeans wear wedding ring on right hand.
Major Pike reveals that a minister on the Swiss border assisted downed allied airmen to escape. If this is true, then "Normandy" would also most likely be true too.
When imprisoned in the castle, Pike and Anna are kept together in a well-furnished room, complete with fresh linens, with free access from the castle's main corridor. Since they're high-value prisoners, it would make much more sense to keep them locked in separate prison cells in the castle's cellars, to make their contact and escape impossible.
(at around 1 h 24 mins) One of the SS orderlies reports to Otto Schack and calls him Gruppenführer, but it's been established that Schack is a Standartenführer. A few seconds later, the next orderly reports to Schack and gets the rank right.
The postcard from Lisbon reads "Sudações de Lisboa". It should be "Saudações" instead.