During the river chase in the second level, Batman hangs from a rope ladder with sharks nipping at his heels. If only he had some Bat-Shark Repellent.
When being taken away by the police the first time around, Joker says, "Watch the suit, boys!" — his first line in Batman: Arkham Asylum.
Lex Luthor consoles Joker about the prospect of Batman being killed by guessing that Robin would probably put on the Batsuit in his place, as in the Battle For the Cowl comic storyline. And Joker replies that it wouldn't be the same, which is exactly the problem he had in the comics.
In the Amusement Mile section of Gotham City, you can find a slide attraction called the Helter Skelter. (This may not count because that's what that sort of slide is called in the UK, hence the name of the Beatles' song in the first place.)
In the handheld version, he even has skeletons as henchmen!
The list of ingredients (promethium, xenon, mercury, tantalum, dialium) that Lex and Joker use to create their fake kryptonite comes straight out of Superman III. The only things left out are the plutonium and the "0.57% unknown".
LEGO Batman 3: Beyond Gotham
In the trailer for Lego Batman 3: Beyond Gotham, the rest of the Justice League are giving their thoughts on Batman's new space suit, Wonder Woman says that he should have stuck with black. Or maybe a really dark gray.