Welcome, my name is XXXXX XXXXX I will do my best to help you with your issue.If the source of the odor has been removed the odor should eventually dissipate. But it will take longer this time of year because the house will likely be closed up more for the winter.
The more fresh air you can introduce into the house the sooner the smell will go away
How do I know if years of a humidity problem haven't caused mold in the walls and elsewhere?
It's doubtful that mold would grow where the humid air can't circulate (inside enclosed partition/walls). Mold usually only grows there due to water leaks. That said unless you have some compelling reason to buy this house then perhaps it's best to walk away given your concerns.
I don't want to walk away. I am looking for some confidence that now that the humidity problem has been removed if the current owner moves his belongings and furniture out and we clean, scrub and paint that the musty smell will go away.
There is only so much I can offer from here. You seem to want assurances I can't give you. All I can tell you is if the source of the odor has been removed the odor will dissipate over time with fresh air circulation. You didn't mention that the house was still occupied with (probably) moldy smelling furniture still there. The current owner's possessions are probably the source of most of the current odor.
You're welcome! I would not be concerned about mold inside sealed partitions if the source of the mold was a humidity problem
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