The ship used in the movie used to be in a boneyard at the Disney Studios Theme Park at Walt Disney World in Florida, where it was an exhibit on the "Backlot Tour".
In a 2019 documentary about the film, Veronica Cartwright recalled a chance encounter that she had with her co-star Matt Adler, who played the role of the older Jeff. On Halloween 2007, only seven months after moving into her present home, Cartwright answered her door to a trick-or-treater and was surprised to find Adler and his young son standing on her front doorstep. Cartwright said she and Adler had not seen one another since the time the movie was filmed, almost 22 years earlier.
Director Randal Kleiser brought in his brother Jeff as the visual effects supervisor, who oversaw the use of reflection mapping software to create the ship's chrome-like appearance. The result was one of the first successful examples of what would later be known as CGI - a full 5 years before the groundbreaking T-1000 of Terminator 2: Tag der Abrechnung (1991).
It was Paul Reubens's idea to make the identity of the actor providing the voice of Max a mystery and he was credited as "Paul Mall".
One of the prop hulls was refurbished, and is now the topper of a drink station in Tomorrowland at Walt Disney World's Magic Kingdom.