When Elio is looking through the Universal Handbook about how to negotiate, the handbook asks him if he wants to foster peace and connection. The symbol shown on the pamphlet is the Vulcan Salute developed by Leonard Nimoy for Star Trek: La serie original (1966) where "Live long and prosper" was a phrase used by the Vulcans, who stand for peace and connection.
Kate Mulgrew voices the narrator in the museum talking about the Voyager space probe. Mulgrew is famous for playing Captain Kathryn Janeway of the starship USS Voyager on the sci-fi series Star Trek: Voyager (1995).
When the audience sees Mr. Melmac in his garage, his shirt depicts the Drake equation, a formula estimating the number of active civilizations in the galaxy. This equation appeared in the TV documentary series Cosmos (1980), created, produced and hosted by Carl Sagan. Sagan (indirectly) plays an important role in the movie.
Elio has a poster above his bed depicting a big number 42. This is a reference to Douglas Adams' novel and eponymous TV series Guía del autoestopista galáctico (1981) and movie remake Guía del autoestopista galáctico (2005), in which "42" is "The Answer to the Ultimate Question of Life, The Universe, and Everything".
Elio's sand drawing that says "Aliens! Abduct Me!!" is a rough sketch of the Pixar campus including the amphitheater.