Water Stains found during inspection - looking for advice

[Waref Hawas]

I'm currently under contract on a property, and I'm looking for some advice. My plans are to live in the property as my primary for a few years and then turn it into a rental. During the inspection, some water stains were found. In addition, one of the water stains had a positive moisture reading. The inspector stated that he's "...not terribly concerned" about this, but that doesn't give me peace of mind. To see if the deal is salvageable, I'm reaching out to independent contractors to have them assess the situation. The property was built prior to 1978 so opening up walls and the ceiling could potentially kick up lead dust. 

Anybody have a similar situation? Any advice on what to do?