In the vicinity of the main room in Alan's apartment, there are at least three telephone extensions on the same line: the red, the blue and the antique telephones. Whenever someone telephones to the apartment, sometimes only one telephone ring can be heard, sometimes two, but never all three.
When Sardi telephones the barber shop, he would have had to ask for Buddy for the barber to pass the telephone to Buddy. But when Buddy talks to Sardi, he refers to himself as movie producer Paul McIntosh of Paramount Studios.