Except for the color scheme, Luthor's flying vehicle looks like the Supermobile, which made its debut in Action Comics #481, from March, 1978, including the extendable fists. (The Supermobile was red and blue, while Luthor's ship is purple and green.)
All of the cutaway gags, and the many forms inflicted on Jimmy Olsen, are references to actual comic book covers from the Silver Age. In some instances, the cover was designed first as a method of luring in curious readers, and the writers had to figure out some way to make them happen over the course of the story, leading to many cases of Superman acting out of character. Most of these were later compiled on a now-defunct website, the name of which Jimmy almost references in the episode, before Lois cuts him short.
In Superman's Fortress of Solitude, a robot from Superman: The Mechanical Monsters (1941) can be spotted.
When Batman goes up against Superman, he's wearing the armor costume that he wore in the graphic novel The Dark Knight Returns. This armor was also featured in Batman: The Dark Knight Returns, Part 2 (2013) and Batman v Superman: Dawn of Justice (2016).