Adam,
I'm really sorry you're having such a rough time with your property manager! Regarding your specific questions, it will depend on what your state laws are and what your contract says. You may have some recourse depending on what those specifics are.
If I were in your shoes I'd two things: first, I'd call your property management company and ask to talk to the managing partner, owner, supervisor, etc. I'd let them know in no uncertain terms that you are incredibly concerned with how they're managing your property, are disappointed in their results, and feel that your manager has been negligent. If they're not willing to deal with you then maybe you'll have to drive to them.
I'd document all conversations and attempted communications with them and call the real estate board. I'm positive that there will be some sort of complaint system in place to handle just this type of thing. I know that our real estate agency is very helpful.
It might also be worth shelling a few dollars and talking to a local lawyer familiar with contract law in your area.
Best of luck and keep us updated!
Mathew