When holding up her arm prior to tossing the hair bomb, the hand Catwoman would be holding it in is completely empty.
While pretending to get out of the yellow net thrown over himself and Robin, Batman accidentally pulls it too high and the actor quickly pulls it back down to cover himself.
The decision to save Batgirl or thwart Catwoman at the Embassy is presented as a catch-22, however, if Batman could send Alfred to save Batgirl, Commissioner Gordon could just as easily have sent a squad of police officers.