The play the inmates are participating in at the beginning is a play by Shakespeare called "The Tempest".
The episode's title "Rogues Gallery" is a reference to the large list or database of villains that Bruce Wayne/Batman will later have as the Dark Knight.
The song playing during the montage of Gordon interviewing Arkham inmates is "Figure it Out" by Royal Blood.
Morena Baccarin (Dr Leslie Tompkins) has a past connection to the Batman Universe after voicing Talia All Ghul in the DC animated movie 'Son of Batman' and Black Canary in Justice League Unlimited.
Morena Baccarin would later star in Marvels Deadpool and Deadpool 2. This adds her to the list of actors who appeared in both, the DC & MARVEL related universes.