When the Catwoman calls Commissioner Gordon to talk to Batman via the batphone, The commissioner activates the phone without any signal noise. Batman automatically picks up the phone in the batcave.
When Catwoman, Robin, and the rest of the gang invade Wayne Manor, Catwoman's goons go straight to the wall safe hidden behind the portrait of Bruce's great-grandfather. Of the six of them, only Robin should know where that safe is, and, as Alfred points out, the drug affecting him blocks his memory.