Make sure your foundation does not have any cracks.
Look for damp spots condensation or visible mould, sewer smells.
Ask you contractor what materials he will be using for the walls, and if he is using a vapour barrier, check that it has been sealed properly all around the outlets and the tops and bottoms of the walls.
If improperly sealed moisture may go into the structure, which may lead to mould growth. Mould growth affects air quality and may lead to health problems.