Bettye's speech about why she went to Columbo mirrors why Don Corleone became involved in La Cosa Nostra in the book - to not have to have their lives controlled by others who cared nothing at all for them.
When Bluhorn grabs Barry in the elevator and tells him "you never show your hand", it is a nod to when Don Corleone tells Sonny to "never tell anybody outside the Family what you are thinking" after Sonny shows interest in Sollazo's drug trafficking business.