Jenny smokes cigarettes in her first scene in a Wisconsin cabin and in her last scene in an Arizona diner, but she does not smoke at all for the three days in between. Very unrealistic. Certainly she would smoke at the diner and at the motel.
Many characters are seen smoking throughout the movie, including a man who picks up the hitchhiking Starman, and the Starman himself (for comedic effect; attempting to inhale makes him cough very forcefully and make faces of disgust). A SETI scientist following the heroes also smokes a cigar, and at one point blows smoke into the face of the show's primary antagonist.