The box the joker grabs a wrench from says "Binford Tools," which is the name of the fictional tool company sponsoring the show "Tool Time," on the Tim Allen sitcom Home Improvement (1991).
This is the first time Harley refers to the Joker as her "Puddin'".
It is revealed that Bullock knows the existence of the Batcomputer, but how he learned of it exactly is unrevealed. It's possible though he just might have been referring to a computer used by Batman as a "Batcomputer" akin to the Batman (1966) TV series habit of everything having a bat-prefix.
This episode is an adaptation two major Joker stories from the comics. The episode is primarily an adaptation of "Detective Comics" (Vol. 1) #475, "The Laughing Fish" and "Detective Comics" (Vol. 1) #476, "The Sign of the Joker," by Steve Englehart and Marshall Rogers. It is also a loose adaptation of the third act of the story from "Batman" (Vol. 1) #251 titled "The Joker's Five-Way Revenge!" by Denny O'Neil and Neal Adams.
This is one of four episodes with no title card, the others being Heart of Ice (1992), The Demon's Quest: Part I (1993) and The Demon's Quest: Part II (1993).