I'm not a naval or structural engineer (but as a chemist, maybe similarly anal retentive). Moisture in core is one of the things I have always been most concerned about. From reading obsessively on the subject, and talking with a lot of people over the years (many of whom know far more than I do on the topic), as others have commented, moisture in core can range from a fixable problem to a showstopper, but it's never a good thing.
A few years ago, I was looking at a late model boat, built overseas. It was only 3 years old at the time, but my moisture meter (yes, I'm anal-retentive enough to have my own, and paid a surveyor to teach me how to use it) showed high levels of moisture in the foredeck balsa core. It looked like the entire foredeck was pretty well saturated, and that it probably came in around around the sampson post that likely was not properly installed. The broker made some vague comments about how a little acetone would 'dry it right out', but I wasn't convinced. I passed on the boat, and then later heard that the sampson post literally pulled out of the deck under strain.
I personally place a lot of importance on structural integrity, especially in the hull. I'm willing to trade off some speed for the extra weight of a solid glass hull, and prefer the security of knowing that if I hit something underway (like those scary mostly submerged railroad ties that I see from time to time), there is hopefully going to be less of a chance of it punching through the hull.
I know David Pascoe is controversial to some people, but I found his writings to be very educational (and also scared me off of cored hulls, and balsa core in anything, for life). Rather than my just parrot what he has written, his website is -
Yacht Survey Online: David Pascoe, Marine Surveyor