For one thing, they can make the Riddler less light-hearted. With Jim Carrey's portrayal, it was almost like having another Joker.
Go ahead and do the riddles and all, but just make him seem like more of a scheming, manipulative type. Batman could think he's figured out, say, two of the Riddler's schemes. Instead, it turns out that they were meant to lead Batman into a third, bigger puzzle. Something like that.