The bust in the Museum of Fame identified as Gotham City's first mayor was previously a statue of The Joker in The Joker Is Wild (1966).
Look for a visual joke in this episode: after the Dynamic Duo escape from the Riddler's deathtrap and return to the Batcave, Batman phones Commissioner Gordon to update him on the latest developments in the case. During this scene, the perspective keeps switching to show Robin pacing back and forth behind Batman at one end, and Chief O'Hara and another policeman pacing back and forth behind Commissioner Gordon at the other.