The film takes place from 1984 to 1986.
Both actors who played DC Comics characters Batman and Superman, Adam West (Batman: The Movie (1966) and Kirk Alyn (Superman (1948)) were performing together as their superhero alter egos did in the "World's Finest Comics" series.
There is a brief shot of a hand moving over a radar screen. This same shot appears to have been reused years later in the opening titles of The X Files