Bill Finger, this episode's co-writer, was the co-creator of many Batman characters; such as Robin, Commissioner Gordon, The Joker, The Penguin and The Riddler.
Batman co-creator Bill Finger never received the credit he was due during his lifetime. While every episode featured a credit saying, "Based upon the characters created by Bob Kane," Bill Finger only got to see his name on-screen in the "Written by" credit for the two episodes featuring Clock King. In 2014, 40 years after his death, Finger's family was able to convince DC Comics and Warner Brothers to give Finger proper recognition for his role in creating Batman and the Batman universe.
There actually was a villain named Clock King in the DC Comics "universe". However, he was a foe of another DC hero; Green Arrow.
One of the "famous paintings" that the Clock King is attempting to steal appears to be Salvador Dali's surrealist masterpiece, "Persistence of Memory". If you'll look closely at this painting, though, you'll see that it now includes impressions of Batman and Robin, being attacked by monsters as they fall through convoluted space! Other pop-culture trivia from this episode: in an earlier scene, the Duo stop by the Dunbar Diner, looking for a waitress named Thelma Timepiece, who used to be the Clock King's moll before she went straight. They're met by a new waitress, who tells them that Thelma quit the previous week, to go "back to her small town in the Midwest"; this is a reference to "Peyton Place". Also in this episode, we learn that Batman and Robin like their Batburgers medium-rare, and prefer double orangeades to wash them down with.
None of the Clock King's Henchmen, known as his Second Hands had individual names, other than numerical designations. Only the Clock King's female Moll Millie (as in Millisecond) was referred to by an actual name)