Uber gives you the drivers name, a picture, and their rating. I believe Uber also gets the person who orders it. Based on their rating the driver can choose to pick them up or not. I believe my rating is alright... My friend just became and Uber driver. I should ask her what my rating is.
One complaint is that a LOT of Uber drivers have no idea where they are going. I've jumped in an Uber plenty of times and when I talk to them they don't live in DC or even frequent it so they go by their GPS regardless of traffic. Multiple times I've given them directions or alternate routes.
People jump into random cars all over thinking they are Ubers. It's just because literally any car can be an UberX. Nissan, Honda, Scion, Chevy, whatever. The only way you can tell if it's an Uber is that it will have the "U" on one of the windows. I've seen it happen multiple times.