Midway through the film, shortly before a series of newspaper headline shots with large 1935 dates are shown, there is an overhead street scene shot with a series of cars parked at the curb. One is a 1939 black Buick which would not have been available for viewing for at least another few years.
While attention to detail of historic 1930s United States paper money is present to a point, most of the bills that Luciano looks at near the beginning of the film are from the 1940s as evident by the signatures and designs.
While Bumpy and Madame St. Claire are listening to opera on the Victrola, the record playing displays the Okeh label. Okeh Records, founded in 1918 recorded mainly middle-of-the road popular music, standards, light classical and blues, but not opera.
An on-screen title card reads "December, 1934", and an exterior shot shows a building with green grass surrounding it, and the sun shining brightly. In New York in December, the ground should be covered with snow. In the following scene, Dutch Schultz is having a meeting while a Yankees game is playing on the radio in the background. A baseball game wouldn't be in December!
The goof item below may give away important plot points.
After Luciano has a hit man shoot Dutch Schultz, the hit man enters Luciano's car demanding payment. Another man in the front seat then turns to shoot the man who just shot Schultz. However, after the first hit man is shot, Luciano is seen raising his hat to cover his face to keep it from being splattered with blood. Raising his hat after the shot is fired is too late. Luciano obviously knows the hit man is to be killed. He should have raised his hat before the shot was fired, not afterwards.