"Okay, Houston, we've had a problem here." The NASA Version
Our problem has very little in comparison with the one Swigert faced on Apollo 13 except perhaps for one thing. It's a systematic problem and it should not be overlooked.
Let's think about what happens when you heat a building (this applies to cooling too).
We can consider two forms of heat loss conduction and convection (we won't worry about radiation) and see how they effect the cost of servicing the building.
Conduction
Some building shell exists (walls, roof, glazing etc) and each of these gradually releases heat proportional to the temperature differential between inside and outside. It is not an instantaneous effect, but is subject to exponentiation. The rate of conductive heat loss is completely unrelated to the rate or temperature at which air enters and leaves the building (ventilation).
Convection
Now lets assume that the building has some form of ventilation. Air is drawn in, used and then rejected by natural ventilation or perhaps driven by fans.
The energy content of air is dependent on its condition (temperature, moisture content and pressure) - this is called it's enthalpy.
When air leaves with higher enthalpy (energy content) than it enters a building, it is carrying energy with it. So with all other things being equal, if you ventilate a building you transfer energy in or out instantaneously.
Conclusion
Now if we assume that a building is maintained in a comfortable condition, we can easily see that the balance temperature (the outside temperature at which we need to attempt no deliberate heating or cooling) is dependent on internal unintended heat gains, on conduction, AND on convection (forced or otherwise).
In short, the balance temperature of a building varies with the rate of ventilation. The fundamental assumption that a building has a fixed balance temperature (essential to underlying theory of degree-day analysis) is flawed if the building is ventilated at different rates at different times.
Offices, Theaters, Hospitals, Sports Halls - All of these are affected.
To point out that Degree-Day Analysis assumes at its' very core that a building has negligible thermal mass (no concrete !), is infinitely ventilated, and has perfect insulation, would be taking this a step too far (though true).
The point made is that Degree-Day Analysis is a very inexact science, based on absurd assumptions that none-the-less provides very useful information if used with sufficient care!
Update February 2012 : You can now get degree-days for anywhere on the planet calculated for free by kWIQly