The clocks in the Batcave indicate that Gotham City is in the Mountain Time Zone, as the Gotham City clock is one hour behind the Chicago clock.
Cesar Romero refused to shave his trademark moustache to play the Joker, so it was covered over by the thick clown makeup. It is clearly visible under the makeup in close-up shots.
The Joker is said to be an expert in make up. According the comic book origins of the Joker (also depicted in other TV/film adaptations) his facial appearance (chalk white face and ruby red lips) were as a result of chemical exposure, not due to any use of a disguising make up.
Only episode in which Dick Grayson was referred to by his formal first name of Richard.
Most of the 'High School students' were in their 20's when this episode was shot.