While filming Um Corpo que Cai (1958), Sir Alfred Hitchcock described some of the plot of this project to frequent Hitchcock leading man and "Vertigo" star James Stewart, who naturally assumed that Hitchcock meant to cast him in the Roger Thornhill role, and was eager to play it. Actually, Hitchcock wanted Cary Grant to play the role. By the time Hitchcock realized the misunderstanding, Stewart was so anxious to play Thornhill that rejecting him would have caused a great deal of disappointment. So Hitchcock delayed production on this movie until Stewart was already safely committed to filming Otto Preminger's "Anatomia de um Crime (1959)" before "officially" offering him the role in this movie. Stewart had no choice but to turn down the offer, allowing Hitchcock to cast Grant, the actor he had wanted all along.
Cary Grant found the screenplay baffling, and midway through filming told Sir Alfred Hitchcock, "It's a terrible script. We've already done a third of the picture and I still can't make head nor tail of it!" Hitchcock knew this confusion would only help the movie; after all, Grant's character had no idea what was going on either. Grant thought the movie would be a flop right up until its premiere, where it was rapturously received.
Sir Alfred Hitchcock filmed Cary Grant's entrance into the United Nations building from across the street with a hidden camera. When he gets to the top of the stairs, a man about to walk down does a double take upon seeing the movie star.
While on location at Mt. Rushmore, Eva Marie Saint discovered that Cary Grant would charge fans fifteen cents for an autograph.
The scene where the crop duster is chasing and shooting at Thornhill was filmed with a real airplane while the shot where the plane crashes into the fuel truck was done using large models of both truck and plane.
Alfred Hitchcock: At around 2 mins, man arriving at a bus stop during the opening credits, but getting there a second too late and the door is closed in his face. He misses the bus.