The restaurant where Joker and his date are drinking a milkshake during his flashback is fashioned after the restaurant in the famous painting "Nighthawks" by Edward Hooper.
When the bat-computer shows the information cards for the Joker and Harley (at around 6:00), it lists Jerry Robinson, Bob Kane and Bill Finger as "known associates" of the Joker, and Bruce Timm and Paul Dini as associates of Harley - their comic book creators.
Zatanna appears briefly but has no dialogue.
Frank the plant says "see you next week on the same Frank hour, on the same Frank channel". This is a homage to Batman series (1966) where episodes ended with "see you next week on the same Bat hour, on the same Bat channel"
After Zatanna frees the Justice League from the Book Of Fables, Flash is traumatized by things being either too soft or too hard, and never just right. He could have been in a twisted version of Goldilocks and the Three Bears.