A good portion of the music when Will is back on Earth comes from Miracle on 34th Street (1947). It is particularly evident near the end when Will and Davey are racing back to the transport point back in town. In the 1947 film, near the end, Susan (Natalie Wood) spots the house she showed Kris Kringle. She yells, "Stop the car...!" and gets out and races to the house. The music is exactly the same.
When Will proclaims the planet the Jupiter 2 crash-landed on is called Priplanus, it's the first time the name appears in the series.
Ruth Templeton is portrayed by series creator Irwin Allen's wife, Sheila Allen (credited as Sheila Matthews).
The Doppler effect (or Doppler shift) is the change in frequency of a wave (or other periodic event) for an observer moving relative to its source. It is named after the Austrian physicist Christian Doppler, who proposed it in 1842 in Prague.