Adam West is the character in peril. This is only one of a few references to the classic 1966 Batman series in the game.
In one of the game's side quests, "A Polarizing Decision", Kevin Smith bemoans being asked to film a fight between Superman and a polar bear. This is a reference to a scene he was asked to write for the canned Superman Lives film.
A side quest in the Hall of Doom has Harley Quinn running a psychiatry booth, for which (according to the name of the quest) she charges "5 Studs, Please". This is a reference to booth Lucy ran in the Peanuts comic strips where she charges 5 cents for advice.
There is a DLC package based on the television series Arrow (2012), featuring a story level, and a selection of characters from the show: Oliver Queen/Arrow, Diggle, Felicity Smoak, Huntress, Slade Wilson, Roy Harper/Arsenal, Sara Lance/Canary, and Malcolm Merlyn.
In Level 1, Killer Croc's henchmen have the same LEGO torso that Killer Croc had when he was a mini-figure.