California Doubling: The entire crop duster scene was supposedly set in Indiana southeast of Chicago, but actually filmed near Bakersfield, California because it's cheaper to film in California than take all the crew and equipment to Indiana.
The California coastline stands in for that of Glen Cove, New York, where Thornhill was originally to meet his fate. The north shore of Long Island is rocky, but not THAT rocky.
Vandamm's house behind Mount Rushmore. Anyone who's been to Mount Rushmore knows there aren't any houses within several miles. Not to mention the topography is all wrong. It does make for a good climax, however.
The final shot of the film was to be the two leads climbing into bed on their train and sharing a passionate kiss with "The End" superimposed over it, but The Hays Code objected, saying it implied that the couple were going to have sex (not an unreasonable conclusion) and demanded a change. In classic Hitchcock form, he obliged and changed it to a cut-away of their train going intoa tunnel.
The studio came close to forbidding the use of Mount Rushmore in the climax. Hitchcock ended up compromising by never showing any of the presidents' faces in the same shot as any violence.
Never Work with Children or Animals: Thornhill is shot in the Mount Rushmore visitor center. After the scene was filmed, one could see that a little boy had put his hands on his ears before the gunfire. Hitchcock proclaimed that after this, he'd just work with people who were either adult or deaf.
Throw It In!: An unintentional one. When Eve shoots Roger in the restaurant with the blanks, a child actor covers his ears before the gunshot happens. The take was still used, since aside from this, it was the best take.
As has often been noted, this is perhaps the closest we got to Hitchcock doing a James Bond film.
Legend has it that Hitchcock denied Jimmy Stewart the part of Thornhill because he thought he was too old for it... so instead he got Cary Grant, who was even older than Stewart. (Another theory is that the less-than-spectacular box office results for Vertigo caused a falling-out between Hitchcock and Stewart, hence no North by Northwest for the latter. ) Other actors considered or suggested for the role included Gregory Peck, William Holden, Frank Sinatra, and Dean Martin.
MGM wanted Cyd Charisse to play Eve Kendall (since she was under contract to the studio) and Cary Grant pushed for Sophia Loren (who he'd reportedly fallen for while working together on Houseboat). Hitchcock also considered Elizabeth Taylor before settling on Eva Marie Saint. Grace Kelly would have got it if she weren't busy being Princess of Monaco.
While the film was still in the early scripting stage, a scene taking place at an assembly line in Detroit was envisioned, where the camera would follow two men as they talked while a car was built behind them piece by piece... and at the end, one of the characters would open a door of the now-finished car and a corpse would fall out! Part of this sequence actually inspired one moment in Steven Spielberg's Minority Report.
Hitch himself noted that he wanted the climax to involve the heroes interacting with the faces on Mt. Rushmore, rather than just climbing around them. Specifically, he wanted Cary Grant to hide for a moment in one of the noses...and then have a sneezing fit. While the scene was filmed on a sound-stage using a model of the monument, so there was no risk of damage to the monument, there was a small public outcry during the film's production, which complained that climbing over the presidents' faces would be disrespectful, so Hitchcock had to agree that the movie would not have characters actually touch any of the faces.
Word of Gay: Martin Landau stated in interviews that he portrayed Vandamm's henchman Leonard as a closeted homosexual who was secretly jealous of Eve Kendall's relationship with his employer. In the scene where he revealed to Vandamm that Eve was secretly working for the Feds, he commented, "Call it my woman's intuition, if you will..."