According to Johnny Depp, the hardest part about working with Marlon Brando was keeping a straight face.
According to Johnny Depp in the Turner Classic Movies documentary on Marlon Brando, when he and Brando are sitting at the table talking about the inconsistencies in DeMarco's character, and DeMarco admits his father was from New York, Depp's lines were rewritten just before shooting the scene, so he had no time to prepare and memorize the lines. Brando talked to the director and cinematographer to find out where the cameras angles were. He then worked out a way in which he cut up Depp's lines in the script and pasted them to the cup of coffee in his hand, then held the cup in his hand in such a way that the camera would not pick up the pasted lines, and Depp could read them.
Johnny Depp agreed to be in this movie on the condition that Marlon Brando was cast in the psychiatrist's role.
The picture that Dr. Jack Mickler looks at in his office is of a young Marlon Brando with his own father.