I just heard this discussion on the air (8/10/2013), and the request for a physicist. I happen to be a physicist, at your service. The glass in side car windows is a special “tempered glass” that is made with internal stresses so that it crumbles into little round pieces when it breaks. The diamond pattern is put in the glass at time of manufacture and is normally invisible. However, Polaroid sunglasses can make it visible. Polarization refers to the direction in which light vibrates: side-to-side, up/down, or diagonally. Polarized sunglasses should be made to block horizontally vibrating light, such as light reflecting off of a road or water, while letting vertically vibrating light through. If you hold up a pair of sunglasses to the light while wearing another pair, you can see the light get dimmer and brighter as you rotate the first pair of sunglasses. Sunglasses held at right angles to each other should block all of the light. Some materials with internal stresses, like the car window, can rotate the polarization of light and act as the second polarizer. The amount of rotation depends on the amount of internal stress at different places in the glass, so the diamond pattern becomes visible when you wear Polaroid sunglasses.
The reason why Polaroid sunglasses sometimes couse headaches is because many pairs are made improperly. Light from the sky is naturally polarized. If the two lenses in your sunglasses aren’t polarized in the same direction, each eye gets a different amount of light and this can cause headaches. Fortunately, it’s easy to test new sunglasses in the store using the crossed-glasses technique.