Stains/scratches on the flooring with a rule next to them so the size is known, pictures of the place being dirty with a statement from the cleaners you hired, etc.  

I walked into a 55k triplex with drop ceilings stained and falling down, rats fighting to get off sticky traps, no HVAC or separate utilities, and the back foundation dropped so much the floor buckled.

Hi Wesley,There are furniture repair finish restoration contractors who use hot melted color sticks and stains to blend scratches in fine furniture. 

Here is my take: It might be time for updates, new LVP flooring throughout (you should be able to get decent quality LVP for about $4/ft installed), online the carpet looks stained, and the edges of the linoleum in the kitchen and bath look grimy; having a patch of carpet in the living room makes the place look smaller. 

They might  see a water stain that could be from 10 years ago....needs to be documented. 

However....the upside of renting is that you wouldn't be doing what we do.... spending much of our time pruning, planting, staining, painting, fixing, remodeling something, thinking about adding something (like..."

If the house has a basement, look for water stains on the basement walls or where the wall meets the ground.

Easily wiped down, stains came right off etc.

I've grown up as a "daddy's girl" and learned many things while helping my father, like how to sand, stain, drywall, paint, caulk, do trim work, and much more. 

I can’t count how many deals I’ve gotten where the original buyer asked for something like carpet cleaning or driveway oil stain removal on a house.