More realistic would be having it host a DB used for differential diagnosis. In which case it could use any readings it gets from the body, or responses to questions, to rule out the unlikely and offer a probable diagnosis. Since no system is infallible, it would need to track answers so that "unrelated" issues could be tentatively removed from the differential.
However, the actual readings you could get from a handheld device would, I imagine, be limited to things like heat, color, and sound. More generally, most forms of radiation/EM waves, vibration, or magnetism, as relevant. So I guess body temperature, infections, discoloration, lungs and pulse, would be the most easily checked.
Disclaimer: /I have zero medical knowledge.