Nobody ever finds the town's doctor. When Mal brings his injured sister to the saloon, Stella sends that blond saloon girl to find the doctor. We never see her again until the end of the movie. Later, Stella herself goes to find the doctor, but then randomly turns up to witness the showdown between Paden and Cobb.
The blond girl does find the doctor in a deleted scene. He's played by Mark Kasdan, one of the writers, which is why his scene was the first to go for time.
Silverado and Turley, the town where John Cleese plays the sheriff, are in many ways opposites of each other; Turley is a place with mostly honest but overly strict law enforcement that, while peaceful, is quite unfairly authoritarian in many ways, while Silverage is a place with a corrupt and lax sheriff that lets criminals get away with their crimes. The ending when Paden becomes the new sheriff implies that Silverado will eventually become something in between, a place with firm but fair law enforcement.