The movie open with the year 1909. A few minutes into the film, Tom and his friend are scurrying up and down an escalator in a department store. Escalators only existed on paper in 1909 and were not in use until about 20 years later when the movie was made.
Near the end of the film, Tom Powers is hiding by the stairs, waiting in the rain for his enemies. After they arrive, Tom stands up and his hat is straight on his head, the next view of him has the hat cocked to one side, then the following view shows the hat straight again.
As Tom and Matt leave the fur warehouse after their abortive robbery attempt early in the film, Matt is clearly seen throwing down his gun on the roof of the building; but after they slide down the drainpipe and run to freedom through the alley both Tom AND Matt throw their guns onto a nearby roof, even though we have already seen Matt discard his.
In the scene where Tom Powers and Matt Doyle are strafed by assassin's machine guns, we see Cagney ducking behind the corner of a building. Bullets suddenly and violently hit and tear up the concrete corner into big pock-marked chips an eye-blink after he ducks. But in subsequent shots, the machine gun damage to the concrete is gone.
The "Foreword" mentions that the movie is to depict "a certain strata of American life." "Strata" is the plural form or "stratum." The phrase should have been written "a certain stratum of American life."
Opening the scene where the building is bombed we see two individuals standing up in an open car preparing to throw the bombs that will destroy the building. They throw the bombs and as the car pulls away both of the bombs have bounced off the building and can be seen rolling in the street immediately behind the car as it accelerates out of the frame and the building blows up anyway.