Revealing mistake: In the shooting scene in the Mount Rushmore cafe, a boy in the background puts his fingers in his ears, because he knows the gun is about to be shot.
Continuity mistake: When in James Mason's house in South Dakota, Cary Grant writes a message to Eva Marie Saint on a matchbook from which several matches are missing. When Ms. Saint subsequently reads the message the matchbook is full.
Trivia: Alfred Hitchcock's cameo comes at the end of the opening credits. He can be seen missing the bus.
Continuity mistake: When Cary Grant writes a message on a matchbook and Eve Marie Saint reads it, the number of lines in the message changes. He writes 3 lines, she reads 4 lines. (01:58:30)
Continuity mistake: When Thornhill is about to be run over by the truck his jacket is covered in dust. When he falls on the ground it's spotless, only to appear dirty a shot later.
Revealing mistake: When Thornhill's cab arrives at the UN there's a couple behind him, a rear projection. Later on, when Valerian's car arrives at the UN the same projection is used, with the couple a mere two meters away form where they were before.
Visible crew/equipment: When the crop duster and the truck are about to explode and the truck drivers run away, one can tell it's not Cary Grant watching the havoc but his stunt double because of his rounder face and slightly different hairstyle. Also confirmed by actress Eve Saint-Marie.
Continuity mistake: When Thornhill watches the road from the crop field, the way he holds the crop and how the leaves bend, differ between the front and back shots. Also, his hands disappear and the leaves swap between dry and green.
Visible crew/equipment: When Thornhill exits the phone booth 6 stage lights are reflected on the glass door.
Continuity mistake: When Thornhill makes a call at the train station the cord of the phone is curled in the wide angle but straight in the close-up.
Other mistake: At the train station, the same red-haired woman in a green dress with two distinctive suitcases appears three times in different places despite her walking the opposite way. Sometimes she has a hat and others not.
Answer: Not really. You could (and at some hotels are still able to) keep your room number private or you could not - i.e. you could ask the hotel staff to keep your number secret from strangers, or you could ask them to tell anyone who might ask. Not having seen this movie, I don't know how likely it would be in the situations you speak of that the hotel guest would choose the latter option- it might be a mistake.
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