Unsurprisingly, I found pills littered all over the room, and food and blood stains on some of the furniture.

Are they going to blame the landlord for hard water stains on their favorite sweater?...

Let's see here....1) A few weeks prior to tenant move-out I send them a cleaning checklist as well as the two pages they signed listing damage and cleaning fees2) I use the same paint colors in all my properties.3) My Clean Magic Erasers are amazing and will remove wall scuffs and random stains. 4) When buying larger items I utilize the Lowe's 10% off trick (spending .99 on eBay to buy a Lowe's 10% off digital coupon and using the code online or in store - this hack has literally saved me thousands).5) At my multi-family properties I include various items near my coin-op washer and dryer: a laundry  table for folding, a roll of paper towels and a bottle of cleaner so the machines can be wiped off; I also include some laundry-related items such as stain remover, starch spray, etc (I buy it from Dollar Tree and it lasts a while - I think the tenants appreciate the gesture). 6) At the Dollar Tree they have a toilet cleaning gel product called Lime-A-Way.

It will get stained too easily. 

I have one that charges an insane low price, can color match stains, and if all else fails patch the stain.Call up apartment complexes and talk to maintenance supervisors and see who they use.

Her responsibility has nothing to do with you keeping the infrastructure in shape.Let me put it this way: If there was a leak that caused $XXXXX of damage to the roof and your tenant "saw a possible stain on  her ceiling" would you say that she was responsible for the roof leak?

Smoke stains are not a known health hazard. 

If smoking does occur on the Premisesor common areas, (i) Tenant is responsible for all damage caused by the smoking including, but not limited to stains, burns, odors and removal ofdebris; (ii) Tenant is in breach of this Agreement; (iii) Tenant, guests, and all others may be required to leave the Premises; and (iv) Tenantacknowledges that in order to remove odor caused by smoking, Landlord may need to replace carpet and drapes and paint the entire premisesregardless of when these items were last cleaned, replaced, or repainted.

Just paintin' er white.My vote is repaint it.Coming from the staining/sealing world, stripping it will not get it all and be a terrible mess and cost a fortune.

I put her in a vacant apartment and the owner even helped move her stuff in there, and she insisted on her carpet being replaced because the plaster had stained it.