The only thing that bothers me a little bit in an apartment I'm considering is a stain on the ceiling of the bedroom.

For example, a roof can have discoloration and stains from a variety of causes.

Grout will stain without sealing every few years.Tile is often additional work and cost.

I agree more curb appeal would come from a paint job, but if newer paint, I would just clean (maybe tsp and light bleach) on half with T-1 11 siding in the photo--maybe the weather side, and roll it out the same color, a fresh coat (or primer, like a fresh start primer, if stained). 

It's usually applying the stain in uniform.

In 6 months they broke 3 light fixtures - I had reports their kids were spraying a garden hose from the outside of the house into the kitchen, broke a large kitchen cabinet door, broke several plastic pieces of a new higher end Fridge, fist sized hole in the wall, carpet stains and the entire house may need another repaint, damaged woodwork, scratched kitchen cabinets, stole the curtain rods, curtains my wife spent a lot of time picking out stolen, destroyed the back yard - let the weeds grow several feet tall in the flower beds etc.  

He even raised an eyebrow when I mentioned I was going to replace one of the (terribly stained) toilet seats for $6. 

I own a small painting business that focuses on exterior painting and staining projects.

I've had house in the past that had 70's carpet without a stain anywhere.

You shouldn't see any dust, just want to ensure the coating will adhere.Apply two coats of FLAT (mutes blemishes) solid latex stain by 3" brush first trimming out edges and casings then rolling vertically with 1/4" nap roller cover.