Very hard to be certain, because potato leaves have nearly as many ways of showing they're not 100% happy as their tomato cousins.
Pretty sure it's not late blight, which has large brown spots which look 'wet', and the spots don't look like bulls-eyes which hopefully rules out early blight.
Could be one of several trace element deficiencies - I'd try a liquid feed which contains micronutrients and/or seaweed extract.
I would also of course be watching them like a hawk in case it suddenly becomes obvious the leaves and stems are starting to die.