Moisture Control Issues:
Before beginning any conversion of basement space into living space, check the basement for leaks or other signs of moisture problems. Because damp basements promote biological growth, including molds, they are not healthy places to live in. Thus, any moisture problems should be corrected before you proceed.
Correcting moisture problems may be as simple as redirecting downspout runoff away from the foundation. It may involve re-grading the ground around the house so that it slopes down away from foundation, or venting the dryer to the outside (something that should be done in all homes). Sometimes, however, there are more extensive problems which can be expensive to correct. In any event, the problems should be addressed before you begin other work.
Radon:
You should test your home for radon.
Because EPA recommends testing for radon on the lowest lived-in level of a home, even if you've previously tested, if you have not tested in the basement, you should test again. Because fixing a radon problem will usually be easier and less expensive before the basement is finished, you should test before you begin your remodeling project.
Ventilation
Good ventilation protects both your health and your home. The basement should be included your home's ventilation strategy. If your home currently has no mechanical ventilation this may be an opportunity to install a system.
Combustion Appliances
General recommendation for combustion safety should be followed. Because you are changing the basement and effecting how air moves in the home, you should have a professional check how any combustion equipment, pre-existing as well as new, operates after you have finished work in the basement to make sure that it isn't backdrafting.
Flooring
Flooring must not only be resistant to harm by water, but should also prevent water which does get on the floor from penetrating to the area immediately below the surface (e.g., the padding beneath a carpet) where it can be difficult to dry and can lead to mold problems or cause damage.
Do not install carpet near water sources or areas where there is a chronic moisture problem such as around sinks, tubs, showers, and toilets. Basements may require special attention in this regard. There are two potential problems with installing carpet on a concrete slab. The first is the possibility that water in the form of liquid water and/or water vapor will come up through the slab, causing chronic dampness in the carpet leading to mold growth. This problem is not unique to carpets, and it highlights the need to address moisture up front.
The second is that concrete slabs, especially those without insulation underneath, are often colder than the air in the basement. In fact this is a situation which may be more likely with carpet which insulates the slab making it even colder. In this situation, moisture in the air can condense on the cooler slab, exposing the carpet to moisture and promoting mold growth.
Windows
Basement remodeling may present a good opportunity to replace old windows with new ENERGY STAR® windows. While costs do not always justify the change from purely an energy savings perspective, there may be other benefits of new windows. More efficient windows may be less prone to condensation and related mold growth. Painted window sashes and frames in homes built before 1978 may contain lead-based paint; this is a special concern because the friction of opening and closing windows can release lead dust into the home.
General Recommendations
You should also review the general recommendations for all remodeling and renovation projects in the guidance "Addressing Indoor Environmental Concerns During Remodeling."