It appears besides popping out and cleaning out the washable filters there are additional recommended maintenance in cleaning the coils and blow wheel etc. every so often.  

I won't be able to get a brad nailer behind the HWH or toilet after they are installed so I'll have to do it while I have the chance.

It's adding A-coil, line-set, condenser, wiring for it all, done.

It appears they installed the new coil on top of the old furnace air handler and blower.  

The house has ducts for a heater but does not have a condenser and coil.

I just had to replace an electric glasstop stove recently, and decided to spend less for the rental property and go with coil burner type than another glasstop.

Inadequate airflow through the evaporator coil can lead to this.

We bled the life out of a 25yr old compressor BUT I had already upgraded the furnace to a Hi Efficiency several year before keeping the old evap. coil in but I had a new evaporation coil ready to go. 

Duct work & a/c evaporation coils need cleaning, carpets & padding are usually toast as is most of the door trim the animal uses to exit/enter.

the vertical and diagonal cracks are concerning, OH is ground zero for foundation problems, I have stabilized several with horizontal cracking and bowing walls, but this makes me wonder if you have footing movement, I know of several homes here in WI that were built on unstable soil that has caused similar cracking, the houses often sink over time. there are methods to circumvent with piers or coils, my opinion is, if the deal is VERY good and you can monitor year to year and the cashflow is your play, its rare that houses fall down, consider the base value as static, dont count on appreciation in the future. you could be ok.