This is the second of three credited appearances Ronnie Schell makes in the series, each time playing a different character. His other appearances occur in Our Daughter the Artist (1965) and Fiancee for a Day (1966). At the time of his appearances in this series, he was already playing a recurring role as Duke Slater in the TV sitcom Gomer Pyle: USMC (1964).
The country Peter Mason, played by Ronnie Schell, has written about is officially known as the Principality of Liechtenstein, so called because, although a sovereign country governed by a constitution and a unicameral parliament, it's head of state is a prince. As of 2023, Prince Hans-Adam II is the reigning monarch. At the time this episode of The Patty Duke Show (1963) originally aired, Hans-Adam's father, Prince Franz Joseph II, was the reigning monarch. The country is landlocked between Austria and Switzerland and is reputed to be Europe's 4th smallest country; only San Marino, Monaco, and Vatican City are smaller.
This is the first of two appearances Mickey Deems makes in the series. In his appearance here, he affects a German accent, playing the eccentric German scientist Professor Schroeder. In his second appearance in Cathy Leaves Home: But Not Really (1965), he plays a doctor and affects no accent other than a common American one.