FBI Director J. Edgar Hoover was behind the biggest law enforcement intelligence failure of the 20th century in repeatedly declaring that there was no such thing as the Mafia.
However, on November 14, 1957 state troopers raided the home of Joseph Barbara in Apalachin, NY where Italian crime bosses from across the country were meeting, and after the historic roundup even the good Director had to capitulate.
Following the Apalachin bust the FBI in 1958 released its so-called Mafia Monograph by which it at long last definitively recognized that “available evidence shows that beyond the shadow of a doubt, the Mafia does exist today in the United States, as well as in Sicily and Italy, as a vicious, evil, and tyrannical form of organized criminality.”
While that may have been a major law enforcement intelligence failure, my vote for the biggest one would be the failure to capitalize on the defections of Whittaker Chambers, Walter Krivitsky, and others in the late 1930's and roll up the Soviet Union's spy rings.
Everyone knew the Mafia existed. The question was whether they has as much influence as they said and did as much damage as they said. The Mafia probably killed 1/4 of the people they say they killed.
I went to college in a small Appalachian town. We had a restaurant that was owned by a guy who was mobbed up but on the run. They knew where to find him but left him alone as long as he bought his food from them.
A friend worked for a radio station owned by some folks in the NJ mob. They were tied in with a clothing store and a restaurant. The store sold Italian suits and I never saw anyone in it but they ran tons of ads between 1AM and 5AM on that station. The restaurant hired nothing but Sicilians right off the boat. It was a big money-laundering and immigration scheme.