We are almost finished with the docu-series "Lenox Hill" on Netflix. It follows a few neurosurgeons as well as an ER and an OB/GYN physician at a hospital in NYC.
I've watched a few of these episodes and have enjoyed them. However, I suspect that the most important questions regarding the state of American healthcare will go largely unanswered (e.g., why is it so expensive?)
My favorite medical documentary remains "Sick Around the World", although after 12 years it is probably woefully out-of-date (hint to documentary filmmakers - we need an update!)