needs to filter the time wasters and tire kickers from the players, and he has three employees whose job it is to do just that. 

Could be leakage, clogged, dirty filters, and electrical (not triggering the condenser hence the refrigerant isn't empty) as well, but inspection should've picked that up.

Some items mentioned include: - Don't pour grease, oils, rice or pasta of any kind down the disposal because it gums up the pipes leading to a clogged sink- Do run hot water down the drain for 30 or 45 seconds after use to help clear the drain after use.I do the same with a quick explanation on how to change out smoke detector batteries (when you install the 10 year, there's no need unless it is defective) the size of the air filter and how often to change it and how to change it out, how to operate the HVAC thermostat to heat or cool the unit.

My main complaint with some section 8 tenants is they are generally a little more needy with things like changing light bulbs, batteries in smoke detectors, changing filters, and other small maintenance items. 

If the rental comes with central air then you could install a more expensive air filter and also maybe run some air purifiers or a mold fogger and see if your cough improves.  

Fire extinguisher is filled, air filters are good, dryer vents clean, etc. 

I will only consider back charging tenants if filters are extremely dirty.

That includes drain cleaning if grease and other stuff is flushed down the drain or cleaning of AC coils for failing to change the filter.

Have your father in law go in with proper notice to check the furnace filter or smoke detectors and take a look at the interior, hope he has keys.. have him take photos of inside and out. 

But honestly, besides the occasional light bulb replacment, smoke detector battery replacement, HVAC filter replacement, your monthly repairs isn't all that much.