Alright, my reasoning for not wanting Catwoman in the third Batman is actually quite simple.
Batman Begins - The birth of Batman, the mob is running Gotham, Batman comes to clean Gotham up, takes out one crime boss, Arkham is set lose, some are captured and put back. Introduced to the Joker.
The Dark Knight - Batman now has a leash on the mob, they can't do anything, they are by no means out of the picture though, they are still in Gotham. (I don't know why someone said they were all gone a couple pages back). And I'm pretty sure they run some things. The Joker is introduced and "helps" the mob with Batman. And according to the trailers, the Joker gives Batman quite the run for his money. D.A. Harvey Dent is also rooting out the organized crime in Gotham, but is changed into Two Face, thus everything basically falls apart, and we don't know what happens to Rachel Dawes, but I'm pretty sure most of us know her fate.
So when all this happens, with the Joker destorying Gotham and causing Batman quite the headache, with the fates of Harvey Dent and Rachel Dawes, the two frontrunners of stopping organized crime in Gotham, I'm pretty sure the mob will become powerful once again, maybe not to their all powerful self, but maybe they regain some power.
Now....some of you guys on here want Catwoman to become the side-by-side villain along with Two-Face for the third movie....now think about that for second please. Catwoman? Two-Face? And all the things that have happened in Begins and TDK....and for a third movie we are blessed with Catwoman's presence? Now come on people! Let's play it smart here.
You can't just put Catwoman in there, especially when you know what happens in TDK.