You'll probably save money paying a handyman or some young person to remove the old carpet and pad.... and we'll go ahead and assume there are pet staining... so make sure you have someone get in there and bleach the floor and paint it with Killz or a product that is anti-microbial.  

agreed with everyone. please never paint brick. it's a nightmare to maintain for the future owners. i believe that if you don't like the color you can stain it with special brick stain. that being said, i agree that a little landscaping and your new windows will make it look great.

So my step-mother thinks that it is as clean as it's going to get and that what remains are likely unremovable stains.  

Highly resistant to water, scratch, stain, and extreme temperatures.

Well they were either there when they moved in, which means it was acceptable to them at move in, or they made the stains so it is not your responsibility.It is a balancing act.

Having small, new things like shower heads that aren't water stained, toilet seats that are new, new or really clean window coverings, clean/new switch covers, programmable thermostat will also set you apart from the norm.

Carpet is shag from the 1970s, and grandma has been unable/unwilling to clean stains out for a few decades now. 

It stains really easily and it's slippery so you would not want it on a floor or bathroom counters.

I spend around 2k a unit for upgrades which include new vanity, replace toilet wax ring and guts, paint bathroom, replace shower/showerheads with low flow water saving ones, paint or stain kitchen cabinets, new laminate counters, tile back splash, paint entire unit a nice neutral gray, and paint all trim white.

Do the parking lot test - are there oil stains and trash?