I don't think that's scale....it would not come off with your fingers and I don't believe it would normally precip out onto the vinyl. Shocking the pool is a painless, inexpensive possible fix.

You really use little if any extra chlorine....it simply stays in the pool at higher concentrations for a while. I'd bring the Cl up to a solid 15 one evening and test again the next morning. If you have a large drop, you'll have found the issue. Once or twice will probably return the water to the crystal condition you had.

Let us know what you find.