I actually thought this was the best episode so far. Mostly because they're developing the characters without shoving the "hey! this is Batman!" down our throats this time around.
Montoya is jealous, so she's got more than just a professional interest in sticking it to Gordon. As for why Barbara didn't ask him about Cobblepot...well, he had just gone through this whole spiel about how he was disgusted at the corruption all around him. So it's easy to imagine that she's giving him the benefit of the doubt.I don't get the Barbara character, I don't get the relationship with her and Montoya, especially as there's a whole scene setting up "Ask him about Cobblepot" then she doesn't even ASK him about it, but seems to assume he's still good... And then Cobblepot TURNS UP AT HIS FUCKING DOOR so what was the point of the whole scene with Barbara and Montoya, trying to sow the seeds of doubt, that just makes Montoya look like a huge bitch...