I think there is just automatically a negative perception of allowing pets due to odors and stains.

.$110/sqft - New, basic finish out, mix of carpet, simple hardwoods, level 1 granite$120/sqft - Nicer fixtures, stained concrete, nicer hardwoods, more complex roof designs and decksThese are all spec prices. 

Use a stain that is dark and actually embraces the dark stains.

Why was there a damaged towel and bed sheet including what looked like grease stains?  

My instinct is to give it back to her in full but there are damages:(1) There is a 3'X3' stain on the hardwood floors that cannot be removed by cleaning/sanding.

It's a hard rule to enforce, increase security deposit or let her know you'll have to take extra measures to ozone the apartment for smoke and other nicotine stains or cigarette damage.

Provide proper notice according to the lease and perform a quarterly fire/safety inspection that includes smoke/CO2 alarms, furnace filters, cracked windows, missing screens, broken locks or electrical or plumbing fixtures, holes in drywall, water/smoke stains on ceiling, missing wood trim or handrails, loose flooring/carpeting, general cleanliness etc.

After they moved out, I learned that furniture was covering stains or they damaged the property as they moved out.

Refinished but not stained.

Keep in mind that Solid Stain is different and falls into a category of it's own.Paint Type: Use water based paint, not oil.