Finished Hospital Station, by James White, the first book in the Sector General series. It's a fix-up of five short stories set in a huge galactic hospital, where patients from many alien races are treated. The staff is also composed of professionals from many alien species.
Because of this series, James White is sometimes regarded as the father of medical science fiction. Although he is no Nobel Prize material, he seems to be a competent writer who knows how to craft an entertaining story. Since it's episodic, this book feels like a TV show, joining medical plot elements with some character work.
The stories are pleasant enough, with a pacifist undercurrent. The author abhors wars, and here the antagonists are normal illnesses, mental disorders and accidents. This is a nice change of pace, but also can be a limitation, because the stories end up feeling a bit similar. White imagines many interesting alien species, but paradoxically he doesn't have a background in medical or biological sciences, and it shows: more than problems of exobiology, we tend to get panicked patients going on a rampage through the hospital (the security there seems to be awful, by the way).
A successful medical TV show relies heavily on the interaction between main characters (doctors, normally). We have some of that here, but I feel the series would benefit from much more emphasis on characters.
It's also a bit dated (the stories were written in the last part of the 50s). As far as human professionals go, the doctors tend to be male and the nurses female.
The working style within the hospital is rather weird. On difficult cases one would expect a lot of teamwork, with interdisciplinary teams. Instead we get a doctor in charge doing more or less as he pleases.
All in all, an interesting sample of a seldom-seen subgenre, but I had the impression that it had potential to be better.