If it's a patient privacy issue, you can file a HIPPA complaint via the hhs.gov website.
If it's a customer service issue you could send a consisely written letter regarding your displeasure.
I don't know of any MSC that exclusively deals with medical labs. The average MSer isn't qualified to determine if a certified lab or med tech is doing their job properly. Jcaho accredited facilities undergo routine compliance audits.
Sorry to hear you received the wrong test kit and had to start all over. It all sounds a bit dramatic and complicated. Hopefully you weren't charged for the unnecessary kit/testing.