Oliver Foley's mother Helen Foley is named after Rod Serling's favourite teacher. She previously served as the namesake of the protagonists of both Nightmare as a Child (1960) and the Twilight Zone: The Movie (1983) segment "It's a Good Life".
It seems that Whipple owns a Cable News Network and also a computer equipment manufacturer, and may be an allusion to original Twilight Zone episode, "The Brain Center at Whipple's (1964)" It is the name of a pinball machine, found in the Oval Office
Wunderkind is German and it literally means "Wonder Child" or child prodigy, as in a highly talented or gifted individual; one who is successful at a young age.
John Larroquette (President James Stevens) previously played a member of the Ku Klux Klan in the Twilight Zone: The Movie (1983) segment "Time Out".