I've only had few problems which needed hospital treatment. The worst one was a chronic infection of my ear that threatened to infect my facial nerve and paralyze my left half of the face.
Eventually after one year of stinking fluids comming out of my ear and 14 ear-specialist appointments I was sent to the hospital where they diagnosed me with the correct disease, Cholesteatoma, and i was signed up for surgery as soon as possible. That just happened to be 6 months later

The surgery went fine but I caught a light infection while recovering
I found out that the ear department of the public hospital here has two doctors. Two doctors!
All in all my impression is that the danish doctors are very talented, there are just not enough and our government won't give them the money they need..