The major problem I had was that the lawyer who found the plans for the Tumbler seemed to know that Bruce Wayne was Batman, which is essentially confirmed by Lucius Fox. All he knows is that Wayne Enterprise provides Batman with his technology.
Actually I think it would be far more likely that Batman is a average/non rich and famous citizen, but is just funded by someone rich, like Wayne.
I was also hoping that Harley Quinn would be in the movie, I was pretty disappointed the Joker didn't have her helping him.
Actually, it's possible that Lucius Fox gave away Bruce Wayne's cover. You're right. At that point, all Reese knows is that Lucius Fox is secretly providing Batman with equipment. It's Lucius that connects the dots for him by suggesting that "one of the richest, most powerful men in the world" is the same man who "spends his nights beating criminals to a pulp with his bare hands." Your bad, Lucius! Take the shame, mate.
As for Harley Quinn, I still think there's posibilities for putting her in a sequel as an obsessive fangirl who sees herself as the Joker's soulmate. Perhaps she can even act as the Joker's surrogate while the Joker is in prison (allowing the Joker to have a presence in the film without recasting the late Heath Ledger).