Principal photography began in August 1957, filmed in Technicolor and Vista Vision, Hitchcock's preferred widescreen format. But let's dig a little deeper here.

From the first moments, NXNW is innovative and sophisticated. It was the first film to use those kinetic title credits that you came to see in so many James Bond films. A series of angled, intersecting lines appear; the credits move across the screen; and the graphic grid dissolves into the windows of Thornhill's office building, reflecting the traffic and people whizzing by on the street below (source).

Parks and Rec

Hitchcock was known for his bold and creative work with the camera, but he had to get really creative for some of the scenes in NXNW. He knew he wanted to start the film with a murder at the U.N., and he'd always wanted to film a chase scene across Mount Rushmore.

But how?

Even Hitchcock didn't have enough clout to get permission to film at the U.N., so he had a couple of cameramen pose as tourists to get some still shots that allowed him to recreate the interiors on the MGM soundstages. He used a hidden camera with a long-focus lens to secretly film Grant approaching the U.N. building and managed get a camera high atop a neighboring building to get an aerial shot of him fleeing the U.N. after Townsend's murder (source).

It's an awesome shot, BTW.

How about Mount Rushmore? Hitchcock had always dreamed about setting a chase scene there. In 1958, MGM and National Park Service officials reached a tentative agreement that they could shoot the scene on Mount Rushmore as long as no violence was filmed on or near the faces and area below or on any mock-up of the monument. But when Hitch let slip to a reporter what his actual plans were for the chase scene, the permit was revoked. He would have to settle for creating a replica, and even then was only allowed to film below the chins of the giant faces.

Here's what Hitchcock told an interviewer:

Now, in that same film there was a final sequence on the faces at Mount Rushmore. Due to the objections of the government, we weren't allowed to have any of the figures over the faces. We were told very definitely that you could only have the figures slide down between the heads. They said this is the shrine of democracy. (Source)

He wasn't unreasonable, though:

In North by Northwest during the scene on Mount Rushmore I wanted Cary Grant to hide in Lincoln's nostril and then have a fit of sneezing. The Parks Commission [sic] of the Department of Interior was rather upset at this thought. I argued until one of their number asked me how I would like it if they had Lincoln play the scene in Cary Grant's nose. I saw their point at once. (Source)

Hitchcock proceeded on a PR tour of South Dakota, assuring the citizens that all he meant to do was to honor their great state and its national treasure. Hitchcock filmed only the scenes in the cafeteria and parking lot on location, and spent $50,000 to build a replica of the monument on the MGM lot. Even then, the Park Service didn't want him to show murder and mayhem on the faces on the Presidents, even if they were replicas.

Hitchcock didn't really keep his promise, as you can see from that climactic scene that includes plenty of violence. He used some of the still shots of the actual monument as the backdrop for part of the chase and used his replica for the rest. Hitchcock even implied during the run-up to the movie's release that the chase scenes across the faces were shot on location.

The National Park Service was not amused. NPS Director Conrad Wirth even demanded the film be recalled, stating, "It is an act of deliberate desecration of a great National Memorial to even imply that a game of cops and robbers, for the sole purpose of producing movie thrills, has been played over the sculptured faces of our most honored Presidents" (source).

But by then, it was way too late. The film had been released to rave reviews, and the Park Service had to settle for removing the credit that acknowledged its cooperation in making the film. Not surprisingly, the film drew tons of visitors to Mount Rushmore—people who probably wouldn't have gone otherwise. That dignified national monument was now part of the popular culture.

Hitchcock's biographer Donald Spoto wrote that, despite what he said to the authorities, he probably never had any intention of obeying any of the Park Service restrictions that stood in his way (source).

Except for that sneeze, of course. That would have been just plain ridiculous.