Bummer. Cleaning is really an art, when you think about it. It's about cleaning the home and beautifying it at the same time. Then you have the cleaner who is a clutz? The next one leaves crooked pictures. I would want to come home and find my home 'lovely'. So, look, a good housekeeper is out there. 'Can' the one you have and ask around, be determined, be willing to fork over the dough because a good one is likely at a premium, both in her time and scheduling.
Your not being too picky. Think about it. The first one is a clutz and you can't have the clutzy cleaner breaking your stuff. The next one can't remember to move stuff back after she dusts it? How hard could it be? If you had a table full of those teeny figurines, I could see it. But when you move a vase to dust, move it back, and, who doesn't like straight pictures? LOL.
I don't live in Phoenix, so can't help you. But I support you in getting a good one.