One of the achievements for the Steam version involves being killed...by Toroko (No, not her enraged version), weakly flailing a stick.
When Quote and Curly reach the end of the Labyrinth, they find a huge rock you can't both open. Balrog shows up and makes his usual threats while an oblivious Curly asks that he help move the rock. He starts doing so...then suddenly knocks both of them back and shouts "ARE YOU EVEN LISTENING TO ME?"
The first time you meet Balrog, he argues with Misery about taking credit for catching Sue. The next time you see him, he seems not to remember that at all when he says Misery was punished for it.
The cinematic in the Egg Corridor where Sue attempts to fight Igor. She uses the fact that she can beat up her wimpy brother as a threat. Igor proceeds to start punching her, and she attempts to surrender at every punch. The squeak sounds made and her expressions/lines are what make the scene funny.
Talk to the mimigas during the battle against the Doctor, one of them will snark about the "interesting priorities you've got".
One of the plenty Easter Eggs has you finding Curly's Underwear. Make of that what you will.