If you are worried about moisture have you used a moisture meter to see if there is a delta between that area and somewhere else on that wall? 

I went over to check it and there is just a tiny bit of moisture at the base.

Anytime you see discoloration on your walls, floors or ceiling it is a signal to address MOISTURE issues.

The builder dried with fans and made sure there was no moisture.

-Has no crawlspace (common for older properties) so we couldn't see the foundation-Drywood termite/wood decaying fungi damage seen on all the windows/doors/parts of the beam on the exterior, parts of roof decking and rafters in the attic-Old leaks/moisture damage seen in the ceilings and attic-Parts of the roof has patch work-Roof doesn't have any permits on record (don't know how old it is)Seller's offer to me:-Fumigation treatment for drywood termites (tenting the house)-Replace and repair all damage wood throughout the house-Replace the entire roof with a new permit-Replace one window in every room (not all)-Pay for a structural engineer to inspect the foundation-Offer to get quotes for repairs and have a 15-20K budget to make all repairs, house is 500K.

LOTS of people in beach markets like mine report the Schlage Encode has issues with the humidity/moisture. 

Sometimes moisture gets under the tile and they lift.

The one I am most concerned with is the moisture stain, were they able to figure out where that is coming from? 

Then you can clean/remove the mold and the problem won't come back.The most common source of moisture is lack of ventilation in the bathrooms or condensation on windows in the winter.

insulate the crawl space to stop rising moisture Did you work with any real estate professionals (agents, lenders, etc.) that you'd recommend to others?