Figured I'd bump this thread since I'm reading the book by Bryan Burrough that the movie was based on.
The book is true and well researched.
The plot is the period from June of 1933 till January 1935.
This is considered the period that made the modern FBI. The period when they were chasing, not only Dillenger, but the Barkers, Bonney and Clyde, Pretty Boy Floyd, Machine gun Kelly, Baby face Nelson, and the shooters from the "Kansas City Massacre, all at the same time, with overlapping trails and mutual acquaintances among the robbers.
The FBI does not come off well, Naive college amateurs is a generous description, and one of the biggest names in "G-Man" history, Melvin Purvis, is portrayed as a self promoting idiot.
The cases were difficult not because a bunch of (JD is the exception ) midwest hicks were so clever, but because the Feds were so stupid.
Excellent book.