Besides Crane's fear glass, the "trophies" that Batman has include the Ventriloquist's dummy, Two-Face's coin, Joker's joker cards, Ra's Al Ghul's blade, and Catwoman's goggles and whip.
Bruce tells Jason that "If this new girl is into cats, run." This is a reference to Batman's romantic history with the villain/anti-hero, Catwoman (whose whip and goggles could be seen on display in Bruce's trophy room).
At 32:40min Crane makes reference to Walter White from 'Breaking Bad'.
Bruce tells Jason that he has to attend a conference call with Metropolis, because "Luthor's up to something." This is a reference to Superman and his arch-enemy, Lex Luthor.
When Red Hood is fighting Hawkins, Red Hood laughs while dodging the attacks easily and says "Try Harder!" a possible reference to the same line in the same type of fight scene in The Crow (1994)