Not to mention how stained they left my carpet.

Damaged parts of the property, curb appeal, look for water stains or running water it can signal a big issue.

I didn't have a rust problem, but I see that the product claims to eliminate rust stains.

They had smoke stains on the walls, burned old blue carpets, pink bathtubs and garbage everywhere but they just trusted that I’d make the old units look like the one I had just finished.

Had he simply said white stain to be removed I would have removed the paint.  

A good choice for a couch may be something stain resistant or with a washable slipcover. end tables, lamps, and accessories you can pick up easily at consignment shops.  

He might also be seeing the sunlight streaks, which COULD be mistaken for cracks or stains across the floor.

If there is a crawl space or basement you can possibly lookup into the ceiling and see the bottom of the floor from below for staining in the wood where it has seeped in.Unfortunately you might need to take down that new drywall you did and check again.

@Heath Thomas Jr, are the existing doors stained?  

We are on well water with city sewers and, other than fighting rust stains  (looking into a dedicated filter right now, maybe I'll post for recommendations) we like it.