When Johnny's girlfriend walks out of the room after arguing with Jeff, she carries her purse and hat in her left hand while the right hand is free to open the door. But on the next when cut you see her reflection through the mirror as she exits the room, the image is the opposite of how it should appear in the mirror.
When Johnny is asking Benjy about the cop who won't let him put in slot machines, Benjy hands him a note with the cop's badge number (#711) on it, which he unfolds before handing to Johnny. Then we see Johnny unfolding it again.
When Johnny is approaching the Fifty-First Ward Social Club right before the gun battle, his tie and shirt can be seen over his scarf. But on the following shot, his tie and shirt are now covered by his scarf.
During the climactic shoot out at the end 4 gunmen produce 5 revolvers for 30 shots total. The 1st man goes down after firing 2 shots. Of the 28 available shots left the actors fire over 34 rounds without reloading. The main culprit is Johnny that produced a 2nd gun after 6 shots but gun #2 fires at least 9 times.
Johnny Eager is posing as a cab driver and talks to his parole officer about missing the old ways and his fancy clothes, etc. Then several times he changes his cabby jacket and tie only to switch back to his gangster persona. He doesn't change his shoes, pants or the shirts he is wearing that have very fancy cuff links which makes the disguise less plausible.
When Johnny is in the office talking about the dog he just inherited, he walks toward a door marked private after the conversation ends. As he approaches the door, the entire audio goes mute for almost two seconds.
When Johnny enters the room where his girlfriend and Jeff are quarreling, he closes the door in a normal fashion but there is no sound of the door closing.