Revealing mistake: As Moe and Cranston chase Khan through the city streets, the view through the rear window of Moe's cab shows the cab doing a sharp turn even though it is driving straight.
Revealing mistake: After Shiwan Khan's goon falls to his death and Moe is looking at the dead body, it is elevated up to the mid-section of Moe's body, indicating the the body was on a table or platform to get a better camera angle of Peter Boyle (Moe) observing the dead body. The shot could not have been accomplished if the body was at ground level.
Revealing mistake: The first time at the Cobalt Club, Wainwright gets a report of the Shadow, and plans a task force. Lamont's face goes dark, and he makes Wainwright forget about the Shadow. After the matter is forgotten, Lamont's face lightens, and you hear the chair he's in creak, giving away that he leaned back out of the light to make the illusion.
Answer: In the comics he was a tall, thin man with a large hook nose, sort of like "Sherlock Holmes." When the movie was cast, they thought of altering Alec Baldwin's face for the role, but decided that all those prosthetics would make him unrecognizable, so it was decided he would morph into the original character, when using his "Shadow" power. The same thing was decided when Warren Beatty was cast as "Dick Tracy."