First of all, the movie is excellent. It is a character piece, so rather than a continuous plot line, time is inconsequential to the focus shifting from one main character to another.
Violence is EXTREMELY gruesome (bullet shot into back of head shown exiting the front, dying man attempting to talk having blood run from his mouth, realistic wounds with blood running until person is dead). This bothered me more than my 14-year-old son. My husband's comment was that when he was our son's age, not much phased him. I think he has become immune through video gaming. If your child is sensitive and easily relates to people in movies or books, they are likely to be bothered by the close-up and realistic violence. Be aware that a woman is beaten up by FBI agents.
There is a stark contrast between FBI agent Melvin Purvis and the criminals he apprehends. He is portrayed as a staunch believer in doing what is right and using whatever he needs to get the job done. However, he is shown as being just, also. When he finds another agent has cuffed a woman to a chair for hours, beaten her, and allowed her to sit in her own urine, he stops the agent, picks up the woman, and carries her away to be treated more humanely.
I'm not sure why other reviews see John Dillinger being portrayed as a likable playboy/celebrity. I thought he was clearly portrayed as ruthless and grandiose. His grandiosity was so great that he made no plans for the future -- tomorrow always comes. At another point, he walks into a police station John Dillinger task force area. There is the contrast of him as intellectually calculating versus Baby Face Nelson who was just plain crazy. He is portrayed as loyal and loving to friends, but this screwed value system adds to his complexity. He rarely shoots others, seems to go out of his way to avoid it. However, lots of people around him are more than willing to do it.
Again, unless you have a sensitive child, I think the cinematography, the editing, and the messages of the story are valuable enough to overcome the extreme, realistic violence.