Many of the scenes from the trailer were not in the movie, including Brad Pitt riding a bike while shooting and Keith David ordering someone to "bring in everyone," after finding out "it's the Smiths".
The shot of the helicopter flying over Bogotá at the start of the flashback sequence was originally used in Clear and Present Danger (1994). For its appearance in Mr & Mrs Smith, CGI was used to enhance it with burning buildings and someone sitting in the rear passenger seat of the chopper.
The trivia items below may give away important plot points.
After the Smiths discover each other's identities, Jane speeds away in the car and John is running after her. He ends up tripping and crashing through a fence, and his gun goes off. The trip was a mistake, and Brad Pitt's reaction, as well as his following ad-lib, "Oh dear God," are genuine.
The original ending featured villains played by Jacqueline Bisset and Terence Stamp. After this was dropped, a second ending was filmed with Angela Bassett and Keith David as the villains. This too was dropped when it was decided that the film did not need a final confrontation with the villains at all.