The tail registration number of Flint's private Learjet changes from ending in an "L" under the jet's engine to an "LJ" in flight.
When Cramden visits Flint at his apartment, Flint's robe goes from being untied and open, to partially closed, to closed and tied, and then back to open.
When Flint flees Natasha's apartment, there are three KGB agents pursuing him. He throws one off the ledge but later there are still three pursuing him - two on the roof of Natasha's building and one on the roof of the small tower where Flint is.
Obvious mannequin when the president's double kidnaps the real president.
When Flint is holding Natasha the ballerina up in the air, the lifting wires are visible behind Natasha's left arm.
In the theater when Flint is performing ballet with Natasha and it shows the audience clapping at the end, the scene is apparently taken from another period film as the characters are dressed in military uniforms and female costumes of the 19th century.
When Flint is first in Cramden's office, the fake-pencil eavesdropping device is lying broken on the floor, but the wire powering the little blinking light inside can be seen running across the carpet.
When Mr. Cramden visits Flint to ask him for help, a crew member's shadow is clearly visible on the wall behind him, as he is being told to smile and lower his hand slowly so he doesn't get bitten by the dog.
When Cramden lights 2 cigarettes, one for him one for her, he is drugged by the laced paper when he smokes it, but she isn't effected by the drugged cigarette she smokes.
When the Flint girls tell Flint they're going to Fabulous Face in the Virgin Islands, one of them tells Flint that it is only a couple of hours from Rio. Rio is over 3,000 miles away from the Virgin Islands. Not even the Concord could fly there in a 'couple of hours'; and the Concord didn't start flying until 2 years after the movie was released.