(at around 22 mins) Cary Grant tells Ginger Rogers that he will always remember her character "just the way you look tonight", evoking a smirk from Rogers. The line alludes to the song of the same title that Fred Astaire sang to Rogers in Swing Time (1936).
O'Toole ends his coerced radio broadcast with the phrase, "Tell it to the Marines." In the English usage of that day, the retort "Tell it to the Marines" meant, "Everything you just said is total bull, and cannot be believed for one minute." So by ending the speech that way, he was telling his American listeners that everything he had just said in the broadcast was untrue. Presumably his Nazi captors did not get the nuance, but the moviegoing audience would have.
Cary Grant thought the screenplay was rubbish, but agreed to do the film because he had been condemned for allegedly dodging the draft in both the UK and the US.
Rogers to German diplomat: "Every time we go to a new country, it falls." The diplomat replies, "Gott sei dank" (German translation: "Thank God").
Released in the first year of the Second World War for the US, this is one of the first Hollywood films to actually mention the word "Jewish" and to deal with the refugee problem.