In The Godfather Part III Calo says to Don Tommasino during their meeting with Michael that "the Corleone's left drugs, so New York is weak, and Palermo is strong."

Does this make any sense? Why would a New York crime family suddenly leave drugs in 1980 during the height of the narcotics trade? Would that not be suicide? The Corleone family agreed on drugs after the Five Families War, and we're supposed to believe that they continued with this extremely lucrative business.

On the Corleone family chart at the senate hearings, some of Michael's men are in jail for dealing drugs.

During the meeting at Don Tommasino's estate, Vincent had become Michael's successor. We also know Joey Zasa dealt drugs, as that is stated several times during the film. And Puzo and Coppola envisioned Vincent becoming heavily involved in the drug trade which would eventually lead to his downfall, and that of the family.