Try polishing the surface. Lots of products to do that, many available at auto body supplies. Could also be moisture under the surface film if the wood is absorbing moisture from the air. Might be getting in through the head of the stock or the butt if those surfaces are not sealed. How's the humidity in your area? Cloudiness might clear up when the weather dries out.

If the side that's getting cloudy is the side you put your cheek on, could be caused by cologne, after shave, or bug spray.