The way Dillinger, supposedly Public Enemy No.1, can march right into a police station of cops who are looking for him, take a look around as if he works there, ask for the score of a baseball game going on and get an actual answer before casually leaving. Who cares whether it really happened or not, that was just cool as hell.
Well he may not have actually gone into the Dillinger Squad's offices, though he did enter that same building while taking Polly Hamilton to get her waitressing license.
Billie is arrested and violently interrogated by a particularly nasty FBI agent. She gives him an address for Dillinger, and when he finds the place empty and comes back hopping mad, she just says that Dillinger is long gone by now, and the agent even walked right past him as he was arresting her.
The scene where Billie is arrested is very accurate, with Dillinger driving away unnoticed while agents were handcuffing Billie.
Not so much the scene where Billie is browbeat, since it is unknown if this really happened or not.
Lets not forget how he breaks out of prison by taking hostages with a wooden gun. More awesome considering how that is how it actually happened.