But are there any medical conditions which might have an unexpected effect on flight safety, which someone who is not a doctor might not think about?
Well done ! In that previous paragraph I think you've covered most of the things most of us would be primarily concerned about !
I would add just two more. The first would be any kind of ANAEMIA. Where the haemoglobin is low, looks pale, short of breath, easily tired, etc etc. Because oxygen diminishes as we climb up in the atmosphere an anaemic person who JUST copes OK at ground level can become very distressed at a normal airliner cabin altitude ( approx 7000 ft). It would have to be
very bad anaemia, though, to preclude a local jolly at around 2000 ft !
The other one to be very wary indeed of is middle ear conditions, such as infections or Meniere's disease. The unaccustomed movements of an aircraft (in all directions), plus the inevitable pressure changes, could give rise to some very distressing symptoms. Might also aggravate motion sickness, and the last thing the PIC wants is anyone puking in his direction !
The point about both these two is that the problems might not be apparent at ground level, and a non-aviation-minded patient or relative might not be aware of the changes once airborne.