[lisalia]

I voted for should, but would sounds equally good in hindsight. So I think the correct choice would be the third choice, 'either'.

I think should works if the condition is spoken with anger and criticism directed towards the doctor. To me, should conveys an obligation and/or expectation. The word 'such' indicates that the doctor was perceived to be of good reputation, which would make diagnosing illnesses his/her obligation to the patient and patient's expectation of him. A scene that would be suitable for this sentence: An unsatisfied patient lashing out at a relative who referred her to the doctor because of his reputation: 'If he is such a good doctor, he should have diagnosed the illness!'

On the other hand, the second choice (would) would be used if the speaker is sympathetic towards the doctor. I imagine it being spoken in a regretful tone. 'If he is such a good doctor, he would have diagnosed the illness'. I feel that this sentence is as sad as sentences starting with 'If only...'.

Please excuse me if the explanation may seem a bit strange; I haven't done any grammar exercise in ages and I tend to rely on 'feelings' for this sort of things nowadays.