But specifically, what problems could be caused by a doctor who successfully completed the required coursework, et al, but who did not believe in evolution?
You're asking the wrong person. I said this was an issue for the Med. School admissions committee, not a scientist writing a recommendation. Contrary to Gore 3000, who believes atheists can't be doctors (!), I'm not at all sure what, beyond anatomy, physiology and pharmacology, an MD needs to know. An MD when practising medicine is not a scientist, IMO his relationship to biology is like an engineer's relationship to physics. An engineer can believe the earth is flat and still be a competent engineer.
My greater concern would be that if a potential student adopts a Weltanschaung that is antithetical to reason and science, what other problems does he have?