I think what too many people are missing is that, although the series is a more light hearted take on The Bat, Batman, for the most part, still plays the straightman in the show. Aside from his batter with Green Arrow, Batman is usually composed and always evaluating the situation. SO he's not dark, gritty and doesn't talk like two cheese graiters being rubbed together. He's still the World's Greatest Detective because he knows when to let the SuperHero shine and he knows when he needs to step up to the plate.
And anyone who doesn't think lightheartedness works with Batman needs to go back and watch TAS episodes with Harly. Oh, who created her?