You might get lucky with one unit with a non-pet but if you scale SFR ( I don't invest in the space ) you will run across pets.For carpets you can get installed a breathable moisture barrier.

Which is builder speak for "Ain't nuttin gonna git wit"....Which is Southern speak for, "The Interior of the home shall remain free of moisture"....We have been using PEX in all our new builds and re-pipes for the last few years.  

Could include heating/air, oven, dishwasher, washer dryer.Rekey locksClean out exit plumbing so the new tenant starts fresh and any hair clogs will be the new tenant's.Make sure fans (kitchen and bath) are functionalFlush and inspect water heater.Check under sinks and around toilets/showers for any signs of leaking/moisture damage. 

In your first picture, it looks like there could have been some moisture on the wood that has a seam.

This can result in energy loss and moisture intrusion.3.There was some settling to exterior concrete.

Stone foundation - these foundations must be taken care of regularly to prevent moisture in the basement area.

what you need is commercial dehumidifier and not lawyer.Approaching any technical issue with law and everything in between would just add to the insurance and headache cost.When you purchase just use FLIR and a moisture meter, a dehumidifier could reduce the effect of the mold issue.

Also how a house smells can tell you a lot about a property, moisture and mold are absolutely things that you want to identify up front.

Moisture just cannot get down to the sub floor. 

You will have to take additional steps for moisture mitigation, egress, etc. which will drive up your costs even more.I would go talk to the city and a local architect/engineer/GC and see if you can get a better idea of how much would be involved with something like this.