Continuity mistake: Thornhill and his mother go to Kaplan's hotel room, room 796, to check the place out. There are two telephones in the room and both phones have old-fashioned non-coil cords connecting the phone and the handset. But when Thornhill rings the buzzer to summon the maid you can see that the phone suddenly has a more modern coil handset cord.
Revealing mistake: When Thornhill is going up the driveway of the house near Mount Rushmore, there are shadows, even though it is night-time! These shadows are far too strong to be moon shadows and there is no source of artificial light that could be making them.
Deliberate mistake: One of Eva Marie Saint's lines in the dining car seduction scene was re-dubbed. She originally said, "I never make love on an empty stomach," but it was changed in post-production to "I never discuss love on an empty stomach." It is said that the censors felt the original version was too risqué.
Factual error: The date shown on the newspaper after Cary Grant is accused of stabbing the diplomat at the U.N. is Nov. 25, 1958. The subsequent outdoor scenes clearly show leaves on the trees and people dressed for warmer weather.
Plot hole: The villains try to kill Cary Grant by getting him drunk and sending him off a cliff in a white Mercedes. He manages to get back on the road and they follow him in a Cadillac limousine. Cary passes a parked police car which gives chase. He brakes to avoid a bicyclist and the police car rear-ends the Mercedes. Immediately a blue 1941 Ford rear-ends the police car. Where did it come from? It would have to have been ahead of the Cadillac and very close to the police car to do so, but it doesn't appear until the moment of impact.
Audio problem: Before the famous attack by a crop spraying aircraft, Cary Grant is set down in the middle of nowhere from a Greyhound Scenicruiser. Another bus, a Flxible BR-29, also stops briefly. The soundtrack of the Scenicruiser's engine is re-used for the Flxible.
Continuity mistake: When the plane crashes into the truck, the bystanders walking towards the scene have shadows, which change angles as you see the next shot. They took them both in the morning and the afternoon.
Revealing mistake: Thornhill & the "Professor" have a chat on the airport tarmack, in which it's revealed to Thornhill that Eve is a secret agent and in danger. At that moment the camera dollies in on Thornhill for dramatic effect. As it does, the distant airplane in the background gets closer very nearly as fast as does actor Cary Grant, revealing that the background in this scene is, in fact, a rear projection on a screen just beyond the actor. (01:40:15)
Continuity mistake: When Thornhill and Vandamm are seated in the café at Mount Rushmore, Vandamm clasps his hands together and rests them on the table. In the next shot, he has his hand flat against his body. In the following shot, his hands are back to being clasped.
Continuity mistake: In the scene on the train in the dining car, the flower arrangement on the table changes. When the shot is over Cary Grant's shoulder the flowers are pink carnations with four large leaves, but when the shot is over Eve Marie Saint's shoulder it's a smaller display of pink daisies with one leaf.
Factual error: At the end the couple are supposed to be returning from Rapid City, SD, to New York by train. The last shot shows a locomotive of the Southern Pacific Railroad. The word "Pacific" on the two locomotives has been covered over (but not on the baggage and four passenger cars visible before fade-to-black). The consist is a mix of SP paint schemes, all of which identify the railroad regardless of names on the side. It would have been easy for them to obtain SP train equipment in LA, but it seems odd that they would have bothered to modify the railroad name on the locomotives, particularly since it changes the name to the name of a another real railroad that didn't serve the US north of Cincinnati and Washington D.C.: the Southern Railway.
Other mistake: When Cary Grant steps down from the bus from Chicago prior to the crop-duster scene, naturally the bus is heading away from his departure point. Later, when he hijacks the car to effect his getaway, he makes a U-turn so that, instead of returning to Chicago, he is heading in the opposite direction.
Factual error: The address of the art auction is 1212 N. Michigan. Michigan Avenue only extends north to the 900 block.
Continuity mistake: As Thornhill backs away from murdered Townsend, the knife in his hand changes from point down to point up. (00:38:10)
Continuity mistake: When the aircraft crashes into the tanker, the position of the aircraft, relative to the edge of the road at impact and afterward, changes several times.
Continuity mistake: His suit changes colour as he is running from the aeroplane. First blue, then brown, then back to blue.
Audio problem: Near the end of the movie when Cary Grant says, "Come along Mrs. Thornhill." If you read lips he's actually saying, "That's it." (02:15:45)
Continuity mistake: When Cary Grant and Eva Marie Saint are riding in the dinner car on the train, there are several instances where the landscape/view as seen from their window repeats itself. Keep an eye out for a bridge they never get any closer to, and a section of tall iron work near the tracks they keep passing over and over.
Continuity mistake: When Cary Grant arrives at the hotel in Chicago, he sees Eva Marie Saint enter an elevator. By looking at the indicator light he sees that she has gotten off on the fourth floor. He would have had to have binoculars to see the elevator indicator light from where he was standing.
Visible crew/equipment: When Cary Grant and his film-mother enter the elevator at the Plaza this is filmed through a glass-door and you can see the reflection of a crewmember in a white shirt who is crouching below or next to the camera.
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.
Blibbetyblip