After Alf asks for his stamps, the polka music in the background includes the NBC theme in it.
David Leisure plays Brandon Tartikoff in this episode, in season 1 he played 'Nicky' ('The Fish') in The Gambler (1987)
Brandon Tartikoff (the real one) would later appear (as himself) in the fourth season entry "Make 'Em Laugh."
The Mr. Welch that Brandon is talking to on the phone is Jack Welch, the head of GE, which owned NBC at this time.