Continuity mistake: Near the beginning of the film, as Thornhill has arrived at The Plaza and is opening the door of the taxi to exit it; visible through the rear window is a red and white Ford taxi, parked behind Thornhill's taxi. Instantaneously, in the next shot taken from the sidewalk, he is shown completing his exit from the cab. Now however, there is a light colored Dodge taxi cab parked directly behind them. (00:04:20)
Continuity mistake: When Thornhill is talking to the maid in Kaplan's hotel room, right after she identifies him as Kaplan, his arm changes from bent over his stomach to straight at his side. (00:29:45)
Continuity mistake: While Thornhill and his mother are investigating Kaplan's hotel room, he decides to try on one of the man's suits from the closet to see if he and Kaplan are similar in stature. He tries on a navy or dark colored suit coat and then holds the pants up against himself to check the length. In the close up of the trousers, they are now a light gray in color. The camera returns to a full shot and, once again, he has the darker trousers in his hands. You can also see the light gray suit in the closet behind him. (00:31:25)
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: The first scene that they show of the train going up the Hudson River is wrong. The hills in the background are much further up the river past Croton NY. When they are eating the train is back down near the wider part of the Hudson around Tarrytown NY. (00:45:25 - 00:47:00)
Continuity mistake: In the very first scene when the train pulls out of Grand Central Station you can see that the sun is setting. Then when they sit down to eat it's the middle of the day again. (00:45:25 - 00:46:50)
Continuity mistake: Cary's position was close to Eva and he almost kissed her, but then his position is farther away when he asks, "Shall I?" Also, in the kissing scene, when Cary is shown he is kissing her near an open door, but then they are against the wall again. (00:53:40)
Continuity mistake: In the last scene before Chicago the train is going through the tunnel at Breakneck Pass north of Cold Spring NY. When they're going back home at the end of the movie theoretically they should be going the same way but they're not. The final tunnel shot in North by Northwest is the Southern Pacific railroad tunnel between Santa Susana and Chatsworth California. (01:00:10 - 02:16:05)
Continuity mistake: At Prairie Stop 21, after the second man arrives, shots on Thornhill show that his left arm is bent (the sleeve is folded), but the wide shot on both of them shows his arms at his sides. (01:09:45)
Continuity mistake: In the scene where Eve writes on the note pad she doesn't write enough. Later you can see much more to the address. (01:20:50 - 01:25:15)
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)
Revealing mistake: Right after Eve "shoots" Roger and meets up with him and The Professor, some of the trees wobble as the ambulance drives past them. (01:46:20)
Audio problem: When Thornhill and Kendall reunite after the shooting, they are obviously on a soundstage and not on location in the wilderness. There is absolutely no background noise, which is impossible in the outdoors: leaves rustling, birds calling, water trickling, wind gusting, etc. prevent the complete silence depicted by the movie. The quality of the actors' voices also sounds like indoors rather than an open space. (01:46:30)
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)
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)
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.
Continuity mistake: When Eva Marie Saint grabs the statue from James Mason and bolts, the spies chase after her. They had no way of knowing she would do such a thing, and yet they are suddenly equipped with long, heavy-duty flashlights.
Factual error: When Cary Grant is attacked by the crop duster, he is supposed to be between Chicago and Indianapolis. Unfortunately, northwest Indiana looks nothing like this. The scene in the movie has miles and miles of treeless landscape. Even in the flattest farmlands of Indiana, there are many visible groves of trees.
Continuity mistake: In the scene where Cary Grant is hanging off Mount Rushmore, and Eva Marie Saint falls and grabs Cary's back pocket, she rips it but in the next scene the pants are un-ripped.
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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