Continuity mistake: When Coogan first meets Julie in the New York police station and puts her coat on for her you can see his cigarette in his hand, then his mouth, then his hand again as the camera angle changes.
Other mistake: When Walt Coogan is chasing James Ringerman on their motorcycles up the stairs, a funny slip up occurs. Ringerman makes it up OK, and Coogan follows him, only to ride headlong into the corner of the stone staircase. He is just beginning to fall over when Director Don Siegel cuts away to the next scene.