During the press conference, the mayor (played by Sonny Bono) refers to two of Sonny and Cher's greatest hits: "The Beat Goes on," when he tells the TV reporter that "The Heat Goes on," and "I Got You Babe," which is what he says in preface to an answer to one of Lois's questions.
There is a reference to the song "You Don't Mess Around With Jim" by Jim Croce in the jail cell scene. The chorus to the song is "You don't tug on Superman's cape, you don't spit in the wind, you don't pull the mask off the old Lone Ranger and you don't mess around with Jim". The prisoner taunts Superman by saying "I'm tugging on Superman's cape". The second prisoner that he accidentally punches after Superman ducks out of the way is named Jim. Another prisoner can be heard saying "He messed with Jim" right after.
Superman's prisoner number was P2450690. He was never completely frisked or fingerprinted during the booking scene.