Factual error: When Robert Kennedy receives news about his brother John's assassination, he is in his office at the Department of Justice. RFK was actually at home eating lunch when he received that phone call.
Factual error: After the interview between J. Edgar and Tolson, they go to a well known D.C. area department store. The exterior of the store shows, "Julius Garfinkle & Co." but on the credit application it reads, "Julius Garfinckel & Co." It was founded as, "Julius Garfinkel & Co." in 1905 even though the owner's name did indeed have a "C" in it.