Like many I don't like how Babs is being here. It's like she's purposely being portrayed as bitchy to make Steph sympathetic.
Also, we see the first clue of the Batcave as the Babs' new center of operations (I think Miller has said this will be the case). Which leads to the questions: Does Steph still not know Bruce Wayne was Batman (even when she was Robin she didn't know)? And Wayne Manor is private property. Does Oracle have a key or has it been completely abandoned (since in the Outsiders, Alfred closed the Batcave off to even Bruce's former Outsiders team after his death)?
And I wonder if Steph was wondering if SHE ever got her costume retired after her "death" (we know she didn't). I assume she thinks Batman believed her really "dead" (right?) so it wouldn't be a totally off-the-wall question to ask.