On top of everything was a plastic sleeve with an old-timey baseball card in it of some dude named Joe Doyle.

I have seen leases for tenants in multi family homes that do not adequately describe the leased space and do not mention the areas such as stairways, decks, patios, lawn etc.

Bought a used stove recently bc the tenant's kid kept breaking the plastic handle on hers and the metal handle ones are way more expensive. 

Also the $20 faucet with plastic guts from the big box store that's on sale may not be your friend.

I would suggest repairing and staining the fence, pressure washing patio and walkway, fixing the blinds that look crooked in almost every picture, and removing the desk lamps in that room.

If the wiring is nonmetallic cable (romex - plastic looking outside layer of insulation) and has a ground wire (3rd wire, bare copper) it might be fine to keep.

One day he wrote an email about the mold and dust and claimed the taped up areas had come loose and the plastic was deteriorating.

Another idea besides a fence for yard sharing is a  little patio for each unit.

We also had an iron tub in the front yard that my mom would fill with water and put black plastic over to help warm the water, then a little hot water from the wood stove, and we would take turns bathing in the great outdoors.Rough stuff, but I don't recall ever being unhappy at that time.

If so, solve it, like keep food in sealed containers, don’t store plastic sodas in the garage (my friend just had critters eat through her Dr Pepper case they accidentally left in her garage).