I believe there is an FBI report that said he had two mentally-challenged children. (I don't know if it's accurate) As you probably know, he married his cousin which was a kind of family tradition.
Also, the FBI believed he helped to facilitate heroin deals for his brother.
In Carlo Gambino's FBI files it said Attorney General Robert Kennedy was very curious about the intermarriage between Gambino's relatives and the NY FBI Office put together a family chart of Gambino's relatives for him.
From the FBI file
"after Attorney General Robert F. Kennedy during a November 4, 1963 visit to the New York field office "expressed an interest in the intermarriage within the blood family of CARLO GAMBINO" and the supposed "resulting imbeciles and morons that have come from such close intermarriage."