Rudi, Sadly, your picture is a bit too blurry to tell what's going on. Are the white spots removable with water? Are they fuzzy? Do they move? A clearer picture would help. Planto

it looks more like mechanical damage, especially if on underside of leaves

this looks like scale to me too. I had this happen to my jade plant. I treated it with http://www.bonide.com/products/garden-naturals/view/025/bon-neem-ii. I spot treated mine with that solution diluted with water and used q-tips. A problem I ran into was if I didn't catch it early enough they were embedded and hard clean off. I used the product above for a while, but when I missed a few days of treatment it had spread to the other leaves, I had to cut off all the leaves of the plant and hope that it would grow back. It did and it's doing fine now. I hope your plant can recover!

Sans, what?! You mean paint can't make babies and spread all over the Op's plant? I'm just throwin out possibilities:). Could be scale. I've been fortunate enough to never have it, but I know they come in all shapes and sizes. With scale I would think it would feel like something when you rubbed your finger over them. You say they feel like nothing. My other guess would be mineral buildup. If this was mine I would take it out of the pot and inspect it. Roots and all. I would get some rubbing alcohol and wipe down every leaf with a paper towel or q-tip. Clean the pot real good, and put in new soil. Throw out old mix it was in. To me it doesn't look like a pest, but I'm not there I can't feel it or really inspect it. It's hard to tell in the pic:). Keep this plant away from other plants:).