If I remember correctly this happens when you place a transparent object between two polarisers, in this case your glasses and the polariser in the LCD (there's actually two in there and are essential to its function). It shows the internal stresses in the transparent object by the minute variations in refractive index, it probably wouldn't show anything if the dash had a glass cover as it would be stiffer and not be bent simply by being mounted in the case.
Another problem that can arise from wearing sunglasses is you can black out the LCD completely if you tilt you head, a 45° angle will usually do it. This is because the light being reflected off the back surface of the display and back out to your eyes is polarised as it passes through the second polariser, and sunglasses block polarised light at certain angles. Line up those polarisers and no light gets through.
By the way, if you want to see stresses in larger object your computer monitor should work too, just open a blank white page and then place the object in front of the screen. Works well with injection moulded items like plastic forks and CD cases.