I write clinical decision support tools, and I interview users (doctors). Nowdays, doctors really just want algorithms to follow. They want to know what the fastest/cheapest way to diagnose problems is.
Frankly, they aren't particularly GOOD at diagnosing problems outside of these kinds of algorithms - for example, a likely cause of many Morgellons' disease cases is actually tropical rat mite (see Nick Mann http://www.telegraph.co.uk/health/8626767/Morgellons-Disease...). Doctors tend to diagnose delusional parasitosis just because it doesn't fit the algorithms.
If doctors are just going to follow a basic set of diagnostic procedures, we can easily automate that using the data that are put into modern electronic health record (EHR) systems. We have your vitals, we know the tests that have been done and the outcomes, and so on. As one (very blunt) doctor expressed to me, doctors just want to follow the diagnosis algorithm, he paid $100k to be a data entry technician, and I think that was pretty much on the money. That's not the only time I've heard that, either.
If doctors are going to be replaced, there's not much that CAN'T. It's just a question of designing a program/robot for the particular task, which is becoming increasingly cheap.