Ironically, because this episode was broadcast prior to the release of Star Wars: Episode V - The Empire Strikes Back (1980), the character of Yoda (who had not yet been revealed to the public) could not be shown, even though he was played by Muppeteer Frank Oz.
This episode was broadcast a few months before the premiere of Star Wars: Episode V - The Empire Strikes Back (1980), and served as an early promotional vehicle for that movie. This is why Luke appears in the Bespin costume from "Empire", rather than the Tatooine outfit that was better known to "Star Wars" fans at the time.
The Star Wars "Pigs In Space" sketch's musical finale is concluded by a brief rendition of the song "When You Wish Upon A Star", complete with a Disney-esque castle and shooting stars in the background. This scene is bizarrely prophetic, as The Muppets were acquired by The Walt Disney Company in 2004, and LucasFilm (owners of the Star Wars franchise) was acquired by Disney in 2012.
The backstage scene where Mark Hamill does impressions of Kermit and Fozzie was inspired by a meeting the actor had with The Muppet Show writers. Hamill recalled in a 2019 interview that Jim Henson asked him if he had any special talents he would like to highlight, Hamill put on a Kermit voice and said, "I've been known to do impressions." Henson replied, "Who do you do?"