While it may be unintentional, having Adam West (the first TV Batman) and Julie Newmar (the first TV Catwoman) play Bruce's parents harks back to the Golden Age Batman, who eventually married a reformed Catwoman.
Kevin Conroy and Mark Hamill (who voice The Phantom Stranger and The Spectre respectively in this episode) also provided the respective voiceovers of Batman and The Joker in Batman: The Animated Series and other productions.
The fake name Batman gives Thomas Wayne, "Matthew Malone", is a reference to "Matches Malone", Batman's frequently used alias when he's posing as a criminal or homeless man in the comics.
Marks the first time in this series that Batman unmasks as Bruce Wayne. Previously, Bruce Wayne has been seen as either a child or with his face obscured by shadow or a mask.
Joker deliberately took control of the crowd's focus, so that they would channel anger at Chill for creating Batman; rather than be curious as to who is under the mask. In other Media Joker loathes knowing who's under the mask; Batman is the masked hero that fights him, not the man underneath.