If you actually took spore samples in many homes that have been owner occupied for years, some of them will have elevated readings that could indicate mold.
Mold is not as much of a problem as making sure that you remediate it property but moreover make sure you eliminate the source of moisture that casued the problem to begin with. Without moisture, mold will never start to grow. So whether it is plumbing, roof, or moisture barriers from the outside that have been breached, you need to get to the source.
Remediation is not a big deal. Find the source, scrub the studs, replace the sheet rock or cabinetry, replace what needs to be replaced, blow the fans, have the company come back and take spore samples to get the new counts. Getting all that done is important but whether you or your wife considers it a show stopper is your own choice. If your wife has a bad feel for the home then most likely it is best to blow it off. Pushing her into something she is only 50/50 on is not what I would recommend.
Termite damage is of a similar nature. Find the source, make sure you take care of it, (tenting or local spraying) and then remediate.
Honestly if you are going to buy an REO then expect this stuff. Your wife should not expect an REO to be in gleaming condition and turnkey ready to go. However these sorts of remediations and repairs are commonplace. Getting them done with qualified contractors will be well spent money out of pocket.
From your description, it does not seem like much of a big deal. Your realtor should be able to make an assessment based on their experience with similar conditions on other homes.
