Last night's big news story here in LA was an alleged sexual assault - by and Uber driver. Because Uber's idea of a "background check" consists of an automated check on whether or not the driver's license put in to the web sore is valid. (Not whether or not it's the person putting it in, of course.)
The big issue is the insurance one, and that's a bigger issue to drivers than passengers, but it's a problem for both. A quarter of California drivers have no insurance. If you are in an accident that is the other guys' fault, Uber's insurance doesn't cover you, nor will your own driver's (since he doesn't have commercial insurance). Good luck with that.