Condensing Potential
When water vapor gets into a building assembly if it hits a cold enough surface it will condense as it is cooled, and if enough of it condenses and stays there long enough, you inevitably get mold. For every building assembly, we'd like to know what this potential for liquid water is.
Every building assembly is built of layers of varying vapor permeability and air tightness and those layers themselves are built up out of pieces, so each layer is not completely uniform, particularly at the joints. When water vapor passes by or thru some layers to a layer of relatively lower permeability, and if that layer is cold, that's where the condensation is. For the complete background see moisture movement.
In a tightly built house the potential for condensation in the envelope (walls, roof) is greater due to generally higher indoor humidity (and due to elimination of dry air moving thru the wall). While older, leaky houses don't have this problem, the tradeoff is that they use more energy, are less comfortable, and often cause dry skin problems in the winter. The better solution is to limit vapor movement thru insulated assemblies, to allow them to dry out when some vapor does get in, and finally to keep potential condensing surfaces above their condensing temperature. Keep in mind however, that most mold problems in buildings are due to air movement, not vapor transport--and when they are caused by vapor movement, the amount of time needed to create the problem is much longer because the rate of moisture movement is generally much slower.
Moisture movement. Moisture moves thru a wall via two mechanisms: vapor transport thru permeable materials, and via humidity carried with air movement. Vapor moves by vapor diffusion thru still air from areas of higher vapor pressure (greater absolute humidity), to areas of lower vapor pressure. Because warm air holds much more water than cold air, vapor most often moves from warm to cold (to move from cold to hot would require the cold side to have a high enough relative humidity, so that its absolute humidity was greater than the warm side)1.
In insulated assemblies, vapor movement is limited by the permeability of the solid materials it must move thru. Vapor is absorbed by permeable materials, infiltrates thru the material and then if the other side contains air (as fiberglass and cellulose insulation do), vapor evaporates into this air. Some materials are more permeable than others: unpainted sheetrock is considered permeable, but most paints, especially vapor barrier paint, will make them essentially impermeable. Plywood and OSB are not very permeable, at least not as long as they're dry. Foams (polystyrene etc) are partially, but not particularly permeable. Asphalt building paper is also only moderately permeable, until it gets wet, in which case it is. Tyvek, an most other housewraps are very permeable.3
Moisture movement carried by air is much simpler: whatever humidity is in the air moves with it driven by pressure differences between inside and out (eg wind, stack effect, or pressure created by mechanical ventilation). Because air movement is due to pressure difference, its direction of movement is dependent on which side has the greater pressure. In the case of wind, air will move into the house on one side, and out on the other.
Of the two, moisture carried by air movement is by far the most dominant: a small difference in air pressure will result in 100 times as much water being carried with it thru a 1" hole than vapor will diffuse thru a 4x8 area of sheetrock. Because vapor transport is so slow, the vapor barrier need not be perfect: as long as the moisture content in the wall stays below the critical point where mold can grow and the moisture has a path the migrate back out in the summer.
Relative humidity and absolute humidity: relative humidity is the percent of water vapor in the air compared to the maximum amount the air can hold at that temperature. Absolute humidity is the absolute amount of vapor in the air (measures in grams water/kg air etc). Air at 0°F and 100% relative humidity, when heated to 70°F will result in a relative humidity of 7%. Air at 50°F and a relative humidity of 100% when heated to 70°F will result in a relative humidity of 50%. In the reverse direction, air at 80% humidity at 70°F will condense at 63°F. This is what causes dew to form on the ground at night. A decent relative humidity/temperature calculator is available at http://andrew.rsmas.miami.edu/bmcnoldy/Humidity.html
What is a condensing surface? because no real world barrier is perfect, some moisture inevitably ends up inside insulated walls. If enough moves thru and hits a surface cold enough, condensation will occur (condensation occurs when the relative humidity hits 100%).
Temperature
Gradient:
To understand condensing potential, you must look at the temperature gradient
across the assembly, which is determined by the distance (in R-value, not
inches) compared to the total R-value. For example, the inside of the
plywood sheathing is R1 from the outside, so in an R11 wall, so it will be at
1/11 of the difference in temperature between inside & out.2
For example, consider the three wall sections, at right with an inside temperature (the bottom of each wall section) at 70°F, and the outside at 20°F. Each has two different cross sections, with different condensing potentials. Looking thru section A for walls 1 and 2, there is little drop across the sheetrock (due to its small contribution to overall R-value), the majority of the temperature drop is across the insulated section, and the temperature at the inside of the plywood sheathing is near outdoor temperature. In wall 3, the plywood is about halfway between the indoors and outdoors (in R value that is, not inches), so the temperature will be close to halfway between inside and out.
Looking thru section B in wall 1, we find that the inside of the outer 2x4 is 70% of the R-value distance toward the outside, so the temperature at the inner surface of that 2x4 will be at the inside temperature minus 70% of the difference between in and out. In section B of wall 2, there is no air, so no condensation will occur in the wall; however because the R value thru section B in wall 2 is so much lower than thru section A (R5 .vs. R11), the inside surface of the sheetrock along the 2x4 will be somewhat colder than the rest of the sheetrock--in cold weather it can be cold enough to cause condensation and hence mold growth. This is particularly an issue with steel studs.
Solutions
The general approaches are to reduce vapor transmission, reduce air leakage, keep humidity low, raise the temperature of the condensing surface and maintain a slight negative indoor air pressure.
Because vapor transport is a slow mechanism, using a vapor barrier paint is a good enough barrier--in some situations even this may be unnecessary (leaving it out would help the walls dry back out). What is important is sealing air leaks to prevent air movement from inside to out. Even though some air leakage will bring cold dry air in, humid indoor air will also leak out.
Air sealing is critical, at least for areas where air can infiltrate thru permeable insulation. Areas of concern are electrical boxes, joints around windows and door, and the joint between sheetrock and the floor. Using a more dense insulation also helps: if you are going to have air leakage, let it be around window & door frames, thru vent holes etc: anywhere but thru the insulated wall.
Because it is difficult to fully air seal a building (in particular a wood framed one), another alternative is to add a low permeable barrier around the house, and make sure the inside of this barrier is never cold enough for water to condense. This is typically accomplished by added a layer of foam board on top of the structural sheathing (for more on how to do this, see the rigid skin construction section).
Using exhaust only fans as a ventilation system will put the house at a negative pressure, which will tend to send any wind forced infiltration out the vent duct instead of thru the walls, but exactly how effective this is isn't clear.
Maintaining a low indoor relative humidity during winter is the de-facto solution, although many people in cold climates using humidifiers to keep the relative humidity from getting too low. While it is a good idea to keep it on the low side, any lower than 35-40% will result in dry skin, dried out mucous membranes etc.
Notes
1: Technically air doesn't hold water at all: water vapor is a gas in its own right and can exist without air. Since we are only concerned with the situation in air, and that air temperature dramatically affects relative humidity, we say that "air holds water", when in fact we are measuring the conditions for water vapor to exist based on air temperature.
2: This temperature gradient is only true if the surface temperature is equal to the air temperature, which often isn't true, but its close enough. As long as the inside and outside surface temperatures change by the same amount (which typically would be less than 10F), the temperature at potential condensing surface changes little.
3: "very permeable" is a relative term, as anyhow who has exercised heavily in a tyvek jacket knows. The level of moisture movement in a house is no where near the magnitude a body puts out.