Diagnosing strange mystery illnesses isn't common, but not doing as well as one could at diagnosing and treating routine illnesses is more common. Automating the diagnosis and treatment process would just be the next step in the evidence-based medicine movement, which is already moving in the direction of having doctors follow best-practice flow charts derived from statistical data.
Doctors do struggle with diagnosing rare illnesses effectively. sometimes with really bad results.
But there's no need for watson. there's already good enough expert systems for this job. for example see isabel healthcare.
The issues in automating medicine are more business and cultural and much less technological.
I absolutely believe that Watson could revolutionize health care, but not in the way most people are suggesting. Despite what you see on House MD, diagnosing mystery illnesses is not something that doctors struggle with.
However, the amount of money that Watson could recover in insurance and medicare fraud would absolutely dwarf what he won on Jeopardy. There's the real payoff...