Other mistake: The second bus in the scene before the crop duster has no license plate.
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)
Plot hole: When Eve is being led out to the airplane, she bolts when two shots are fired from inside the house (presumably Anna firing at Thornhill, not realizing that the gun was loaded with blanks). Moments later, she jumps into a car driven by Thornhill, and they escape together. There is no way Thornhill could have gotten there that fast, given that he was in the house only seconds earlier.
Continuity mistake: On the patio outside the restaurant at Mt. Rushmore the professor goes inside first. His shadow falls upward to the right, there is no glare on the upper windows and no building shadow on the ground. Thornhill walks in seconds later and his shadow falls downwards to the left, there is a strong glare on the windows and the building casting a shadow on the ground.
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.
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.
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.
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: 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: 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.