Agent 23 tells Max that assassinations are prohibited by Executive Order 12333. Order 12333 was in fact signed by President Ronald Reagan in 1981 and had a broader purpose to require coordination between the Federal agencies and the CIA, but did reiterate an existing policy against political assassinations.
In the Latin American dubbed version, Agent 86 is voiced by Mexican actor Jorge Arvizu a.k.a. "El Tata," who also played the voice of the original Maxwell Smart in the Get Smart (1965) television series. Following his style, the dubbed version includes many local puns and colloquialism.
In the opening scene, there is a picture of a wanted criminal on Max's refrigerator. The name of the criminal is Mr. Big, which is the name of the first villain in the original series Get Smart (1965), and the photograph is a one of Michael Dunn, who played the role.
The five-minute skydiving scene, where Maxwell Smart falls from the airplane, and is saved by Agent 99, was actually shot in real-life. Led by Norman Kent, a world famous skydiving photographer, a team of professional skydivers shot the entire sequence over a total of seventy jumps during a four-week period, always jumping during sunset and sunrise, to keep continuity in the scene.
There were several Second City alumni in this movie. Steve Carell was a member of the Chicago troupe in 1991, as was Bill Murray in 1973, Alan Arkin in 1961, and David Koechner in 1994. Nate Torrence, who plays Lloyd, was a member of the Cleveland and the Los Angeles troupes, and was also a member of the Groundlings.
In the skydiving scene, Fred Whitsitt was acting as a stunt double for Steve Carell. At every jump, Whitsitt would carry a custom-made skydiving rig hidden under his jacket. When reaching the right altitude, the jacket would open on his back and allow the parachute to be deployed.
In the first scene in CONTROL's board room, Max plays the intercepted audio of a conversation about decaf coffee and muffins, and he simultaneously translates it to English. The original conversation is in Persian.
Max's pseudonym when he infiltrates KAOS, "Nudnik Shpilkes", is actually two Yiddish words that have crept into the English language. "Nudnik" means an annoying person (like the word "noodge") and "Shpilkes" means impatience or agitation. An appropriate description of Max at that point, from KAOS' point of view.
The trivia item below may give away important plot points.
Other nods to the original show include: Agent 13 hiding in an unusual spot (he hid all over the place) and his habit of crying (Ship of Spies). The question (and rather crude joke) of whether the Claw might be "the Craw," as it was not easy to tell which he was saying. The series of opened doors that lead to the phone booth entrance to Control. The phone booth rapid elevator; Siegfried's line "Schtarker, this is KAOS, we don't (whatever it is) here!"; the dog named "Fang" (in the original series, he was an agent numbered K13). 99's deep infatuation with Max. The Cone of Silence not working the way it was supposed to (only did once in the original series, but the chief got trapped beneath it). The shoe phone. The lines, "Sorry about that, Chief," "Would you believe...," "the old (something) trick," and "missed me by that much." The bomb in the piano. The old German driver shouting, "Dummkopf!" Max getting caught in the final sliding door in the entry hall, when it does not close right away, and he went to check it (although, in the original show, he only got bumped in the nose, not crushed as in the film). The three cars driven by Max at various times in the opening credits of the series (a Sunbeam Tiger, a VW Karmann Ghia, and an Opel GT) appear in the film as well.