North by Northwest (1959)

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.

[Roger Thornhill's matchbook carries the initials RoT.]
Eve Kendall: What does the O stand for?
Roger Thornhill: Oh, nothing.

Trivia: In the scene when Cary Grant is going up the steps to the UN, Alfred Hitchcock shot it from a rug truck across the street. He wasn't allowed to shoot the front of the UN. If you look closely, you can see a security guard in the left corner.