I'll throw in my $0.02.
Age and fitness are two separate issues. You can be older and in good physical shape and you can be young and out of shape. The real question is what physical shape is your father in, and his underlying physical activity is a better predictor than just age.
The first concern is what is his cardiac history? If he has had a cardiac event such as a heart attack or heart surgery he would need an evaluation from his cardiologist. The MD does not have to be trained in diving medicine, just needs okay that he is physically fit to participate in mildly strenuous physical activity.
If there is no cardiac history is he on any medications? As long as it is blood pressure and cholesterol meds and he is stable and well managed without side effects then he is okay to dive as long as he is physically fit to do so.
If he is on diabetes medications then it is a relative contraindication. It will increase his risk since going into a low sugar coma, and if happens while diving would be a fatal event. Many doctors these days will clear a diabetic as long as the meds are stable and the diabetes is well controlled. Personally, the photographer on one of my dives in Hawaii was diabetic, and I noticed she had an insulin pump.
What is physically fit? Good question. The minimum activity for moderate physical activity is 4 METS which are metabolic units. The equivalent activities would be walking 18 holes of golf, carrying 15 lbs up one flight stairs at brisk pace, or sweep/vacuum whole house without difficulty. If your father's exercise is well above this than he should be just fine to dive.
Check out Dive Training Magazine this month. Ironically it is about divers of a certain age, in other words older divers. They may need little more help with the weight of the gear, may be a little slower, more susceptible to cold, but generally speaking if in good physical shape can enjoy diving too.
Good luck.
