Hmmm...this scene with Jim and Babs actually has me debating whether or not I should buy Blackest Night. Arrg.
I think we're supposed to assume now that every main Justice Leaguer knows who Oracle is, though I don't think that's a great idea. One of my biggest problems with Identity Crisis was that Jean Loring, of all people, knew who Tim and Jack Drake were. It makes no sense for the Atom's ex-wife to know the secret identity of Robin when that particular Robin didn't have a big public connection to Bruce Wayne.
(It also had Ollie going on about how Batgirl being shot meant that all the heroes started thinking more carefully about whether or not their love ones were endangered by their work. Which also doesn't add up logically, given that most people wouldn't have known who Batgirl was, and that Babs wasn't shot because of her identity as Batgirl.)
At least here there's a closer connection: Dinah --> Ollie --> Hal. Dinah might not explicitly tell Hal who Oracle is, but Ollie might assume that since Dinah trusts Hal that either he'd know who Oracle is, or that it wouldn't be a big deal if he dropped that knowledge.
If my to-do list tomorrow cooperates with me, I'll try to post some Jim Gordon being awesome with Gotham cops. I've been meaning to post some of it for a while now.