Unfortunately, I noticed the other weekend my dash began to have a few shiny spots that were slightly sticky. Then, last weekend driving around in the hot sun I noticed the full-on problem that matches the picture a few posts back almost exactly.
I looked around the house to see what I have and found this:
http://s7d9.scene7.com/is/image/BedBathandBeyond/47601940014500p
Reading it carefully it says it's safe for using to remove bugs and tar from paint, so I figured it can't be THAT harsh. I tested on a small part of the dash on the far passenger side. I sprayed it on a blue shop towel and worked it into about a 2x2 inch part of the dash, scrubbing with decent pressure (but use common sense here). I then wiped it down with a water/dish soap (only a little) combo, followed by water only. Then dry w/ microfiber.
Parked the car in the sun for a few hours, and to my excitement that portion stayed matte and non-sticky. Did the rest of the dash successfully after that. Now we'll see if it lasts, but it only took about 20 minutes to do the whole dash.
I don't know if it would have any ill-effects if left on for a long time, but again, use common sense here and should be okay. The rags did not have any dye or anything that appeared to come off of the dash, other than some dust/dirt stuck to it.
Try at your own risk. It seemed to work (at least for now) for me.