Frasier declared to Sam his father passed away. When Sam visits on the TV show Frasier he explains he was angry at his father over a fight they just had and told everyone he was dead.
Mr. Reinhardt is played by actor Daniel Davis. He would go on to appear on the series "Frasier" as Dr. Shafer in the Season 10 episode, "Rooms with a View".
Vito says he is taking Carla's daughter to see 101 Dalmatians. 101 Dalmatians was re released in winter 1985, shortly before this episode aired.
The episode title refers to "The Peter Principle," a theory that states that organizations tend to promote people into positions they are incapable of filling, leading to people "rising to their level of respective incompetence."