When Harley Quinn is leaving the police precinct, she points to a wanted poster and says, "Hey, I know that guy!". The wanted poster is that of Captain Boomerang, with whom she worked in Suicide Squad (2016).
Jurnee Smollett does her own singing in the film. Director Cathy Yan hired her before knowing what a proficient singer she was.
Harley adopts a hyena in this film as a pet. In Batman (1992) and the comics, she kept two hyenas named Bud and Lou (named after comic duo Bud Abbott and Lou Costello).
Dinah Lance - aka Black Canary - has inherited her powers from her mother. This is a nod to the comics, where Black Canary remained active and youthful for so long that DC retconned there to have been two: a mother and a daughter, both named Dinah.
When Harley remembers her heart being broken before she met the Joker, she recalls two guys and one girl - and the girl is animated in exactly the style of Poison Ivy in Batman (1992).