At around 29:53 you can see a model in the background of Wills room that is very similar to the famous Robbie the Robot. Robbie appeared in the 1956 film Forbidden Planet and appeared in two original Lost in Space episodes "War of the Robots," where Will finds and repairs him, and in "Condemned of Space" as a guard equipped with a freezing gun aboard the prison ship.
In this episode, it's discovered that John's military affiliation was as a U.S. Navy SEAL.
The woman impersonating Dr. Smith reveals her name as "June Harris". In the original series, June Lockhart played Maureen Robinson, and Jonathan Harris played Dr. Smith.
The model Will is building contains parts of a 1:72 model kit of an 'Eagle' from Space: 1999 (1975).