No Women Until 1972
During J. Edgar Hoover's tenure, there were no women FBI agents. Any female employees of the FBI (non-agents) had to wear skirts or dresses and heels. After Hoover passed away in 1972, the FBI Academy immediately admitted two female agents: Susan Lynn Roley and Joanne Pierce.
Song Investigation
The FBI spent two entire years in the 1960s investigating a song. The song was "Louie Louie" by Kingsmen. The rumor was that it contained pornographic language and concerned parents wrote in to the FBI to have the song looked at. The FBI released a 120-page report saying that there was no pornographic language.