A shoeshine man at Logan International Airport was arrested yesterday on drug charges for allegedly offering customers a puff along with their buff. Anthony D. Scott, 47, of 170C Westview Ave. in Dorchester was charged with three counts of distribution of marijuana after a monthlong investigation by state police and federal agents, said David Procopio, a state police spokesman. Police arranged the sting after they were tipped off that Scott allegedly was selling small quantities of pot at a shoeshine stand in Terminal C, Procopio said.