When Commissioner Gordon calls Bruce to inquire about the stolen sarcophagus, Aunt Harriet exclaims in surprise "What would he want with you, Bruce?" However, it is well established that the Commissioner and Bruce Wayne are close personal friends who frequently see each other socially, so it should be no surprise for one to call the other.
In the batclimb scene, as Suzy Knickerbocker leans out of the window, her earrings hang to the side rather than downwards, revealing the camera trickery. This may well be deliberate, however, given the show's tendency to poke fun at itself.