Plaster mottling is usually an appearance problem, not a function problem. Whether that means resurfacing or not is up to you.

However, a lot of plasterers don't guarantee mottling won't happen. And there's a LOT of debate about why it occurs (workmanship vs materials vs pool chemistry).

Copper may generate blue, blue-green, or even black stains . . . but not brown.

You can try putting Vitamin C on the discolored areas, as well is Iron Out. If it's copper, one of those will lift it off.