Factual error: While hanging from the top of the Empire State Building, the sailor looks straight down the side of the building, which is shown to be flat. This is wrong. From the observation deck, there is another level that sticks out below, where the lights that shine upwards are stored.
Factual error: The guns Lamont Cranston uses in his "The Shadow" persona are Lar Grizzly MK1 Longslide. The movie is set in the 1930s and the pistols weren't developed before the early 80s.
Factual error: In the water tank sequence, Lamont takes a breath through one of the bullet holes. At more than five feet below the surface of water, the human diaphragm cannot push against the water pressure surrounding the chest, making it impossible to take a breath normally. Lamont should not have been able to draw breath at that depth.
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."