Near the one-hour mark, Capone talks to his butler on the phone. He fires his gun, and the upper part of it slides back, indicating that it's empty. A few seconds and a cut later, however, the slide is back and he fires more shots with the gun, even though he had no opportunity to reload.
As John Dillinger's brother enters the Biograph Theater, an agent yells out "FBI". On July 22 1934, the agency was known as the Bureau of Investigation (BOI). It wasn't until July 1935 that it was renamed the Federal Bureau of Investigation (FBI).
John Dillinger was shot in the alley outside of the theater, not as portrayed in the beginning of the film as having been shot inside of the Biograph theater.