1) People loved John Dillinger (and the other depression era bandits) because he robbed the very banks that were seen as driving people to poverty. From Slate:
Americans understood Dillinger, applauded him, and cheered for him because they saw him less as a gangster than as an outlaw—a social bandit of the Great Depression who turned his guns against the banks. Newspapermen in 1934 compared him to Jesse James, not Al Capone, and certainly not to mobster Frank Nitti, who makes strange, gratuitous appearances in Public Enemies. At one especially telling point in the movie, Purvis tells Dillinger that he is about to extradite him to Indiana. Dillinger thinks about it and says coolly, "Why? I have absolutely nothing I want to do in Indiana." It's a great scene, but the spirit of it is dead wrong. Not only is it wholly made up—the two never met—but Dillinger, a scrappy heartland renegade, would never have dismissed his home state.
2) John Dillinger could not have existed without the Great Depression. From the Variety review:
The specific sociopolitical conditions of the time are crucial to the story, but one big thing almost entirely missing from "Public Enemies" is the Depression itself.
3) Melvin Purvis' most interesting battle was with J. Edgar Hoover himself. Hoover, the paranoid narcissist that he was, saw in Purvis a threat that needed to be knocked down. To that end he threw up roadblock after roadblock in attempts to cut the man down, eventually forcing Purvis out of the FBI. It's a wonderfully vicious tragic story that I don't see being captured by the uber-dedicated Christian Bale.