By all means alert you surveyor to anything you specifically want him/her to cover. But I shouldn't worry too much - surveyors love a damp-meter!
He/she SHOULD also advise you of the consequences of what they find, but in my experience some do, some don't. If they don't, then ask them about...
Like you I get surprised that sellers don't reduce asking price a little at a time. But could be that they have found property that they desperately don't want to lose and therefore desperate to sell quickly. Reducing asking price to 300 rather than 325 brings in a whole new bunch of buyers...