They won't pass peeling paint or damaged stucco/siding or a roof that is failing though. 

Hey MattI’m one of those guys that had hangups when someone mentioned vinyl flooring because it raised images of that cheap, peeling laminate that was easily cut and invariably began pulling up, flaking and cracking.  

You'll spend more time and money trying to mask it. 

Peeling paint, cracked window, wobbly handrail, crumbly cement steps, temporary (adjustable) lally columns, knob & tube wiring, etc.3.

Lead-base paints never really bother me unless they're chipping or peeling at which point I simply prep the area scrape any loose chips from the surface while keeping the area well ventilated, clean up any debris, primer over it once that's done and cover with paint...problem solved.

No chipping or peeling after a few months. 

Gfi around sink  , peeling paint, carbon monoxide detector, smoke detector and other common sense type things.  

 You are going to find many situations on where claimed numbers are not how they truly are is once you start peeling back the cover of economic and physical occupancy current standings.

Check your roofs to make sure they are in good shape, the first picture you showed is the gable end of the house with 2x4 fly rafters holding your fascia, the plywood you see is the sheathing for the roof. the paint peeling and mildew would not be caused by something inside the house, but something to do with the temperature and the roof, make sure your roof is ventilated, it appears there are no vents for this roof, 2nd picture shows your soffit with the roof rafters and next to the house is closed up. drill a hole in between each rafter the size of a round vent ( 2 - 3" ) and install round metal vents. at the ridge of the roof, remove the ridge cap, install a ridge vent and recap.

Hopefully your situation isn't that bad.BTW - you should have a respirator (not just a surgical mask) that's designed for mold.