I don't like thinking of Catwoman as incidental either, as I loved her in this. I doubt it would ever have occurred to me how easy it would be to remove her, had others not mentioned it.
I found the whole business with the pit to be superfluous, and if anything were to be taken out I would vote for that. The fact that is was halfway around the globe (something I don't even think I picked up on initially) just made it more distracting. I also didn't feel the pit was well enough visualized to get the point across. I mean he's climbing up a wall... then suddenly he's on top of a ledge (we skip over him climbing toward it) trying to jump onto another ledge. No clear indication that protrusions from the wall would suddenly stop, forcing him toward the ledge. I think it's that whole chunk of the middle act that leaves me feeling like I still don't (really) understand what all the chanting was about. ("Rise." Okay. Apparently that was it)