This depends a lot on the practice. Typically billing and admin are separate, so that people who are in charge of hiring/firing and tracking are independent. If you feel that the practice owner might defraud you in any way, this is a major issue and I would move on. More commonly, the billing department isn't out to get you, but is really incompetent and makes lots of mistakes. This is EXTREMELY annoying and also EXTREMELY common. There are no obvious solution other than double checking everything either yourself or outsource it.
In a conventional business, staffing cost to keep track of revenue streams is thought to be part of cost to run the business. If you have concerns, I would discuss this with the partner in terms of systems level improvement, since it does affect the bottomline for the practice. If you bill fewer RVU you receive less. If you are on a partnership track, I favor open accounting whenever possible, so you see how much you are receiving in billing, and what is the actual amount paid out for overhead. If you work for a facility, it's often a take it or leave it situation. In that scenario I would consider keeping a rough log of daily visits. Large discrepancies should be detected and corrected early. In private practice, I keep meticulous logs of all my billing and account receivables, even though I really don't have to and can use my bank statement to file schedule C using cash (as opposed to accural) accounting. I personally think it's important because audits from various players can occur at any time.