Near the end of the game, Hugo Strange says "This is just the beginning", a line said near the end of Attack of the Clones by Count Dooku, who Corey Burton has played.
A subtle one: Joker attempts to force Mr. Freeze to develop a cure for him by holding his wife hostage. Joker is voiced by Mark Hamill, whose first voice in Batman: The Animated Series was Ferris Boyle, the guy responsible for Mr. Freeze, and Mark's performance as him also landed him with his voicing The Joker in that series. Furthermore, by reading one of the riddles called "Who can BOYLE and Freeze at the same time?" and listening to the Mr. Freeze audio tapes, you find out that Ferris Boyle is canon in the Arkhamverse.
MPT Anne Bishop is voiced by Kimberly Brooks. Given the character's looks and personality (her first question when Batman rescues her is where's Riddler, clearly intending to remove his spine), chances are that Ashley Williams will come to mind.
Beam Me Up, Scotty!: Many have misquoted or misinterpreted Mark Hamill as saying this game will be the last time he plays The Joker. He clarified that what he meant was he wouldn't continue playing The Joker if he felt that he couldn't top his performance, he wanted to leave on a high note. He has since played the Joker again on multiple occasions.
Blooper: As the generator slams Clayface into the Lazarus Pit and explodes, the vial holding the cure is in Batman's left hand, but when he comes to, it's in his right one. Until Arkham Knight confirmed the Joker died, some people speculated that it was intentional, and the Joker took some of the cure and was faking his death. After Knight, though, it's become clear that it was indeed a screw-up.
Development Gag: At one point, Batman overhears thugs talking about the rumor that Harley Quinn used to be a man. Harley Quinn was actually motion-captured by a man, and they even released a fake reveal trailer to tease fans about it.
Nolan North voices both The Penguin and provides the voices of several randomized inmates. It's not unheard of to hear Nolan North berating his Mooks about how much they suck, only to hear Nolan North reply "You heard Penguin! Let's move!"
Hush, who has being-Bruce-Wayne's-evil-double as part of his gimmick, is also voiced by Kevin Conroy.
In an interview, director Sefton Hill said they wanted to include a reference to the infamous Bat-Shark Repellent Spray from the Adam West seriesnote Reportedly, when confronted by "Tiny" in the Iceberg Lounge, Batman would break out the repellent... then open it up to reveal a set of brass knuckles, but ended up nixing it because they felt it was a Level Breaker. There's still a subtle reference; if you get killed by the shark, one of the possible hints reminds you to remember Batman's shark repellent: a flurry of blows to drive it off. In one room, you can listen to the Riddler mutter about ways to take down Batman, and ponders taking Penguin's shark, only to say that there are "too many variables", and that Batman likely has some sort of "shark contingency".
Arkham City was released the same day as the Animated Adaptation of Batman: Year One and shares a lot of the same voice talent: Grey DeLisle (Catwoman, Vicki Vale, Stacy Baker, Martha Wayne) is Barbara Eileen-Gordon and Vicki Vale, Steve Blum (Killer Croc and Sickle) is Stan, Fred Tatasciore (Bane, Solomon Grundy and Mr. Hammer) is Arnold Flass and Johnny Vitti, and Danny Jacobs (Victor Zsasz) is Flass's lawyer.