I had potatoes just like that last year. They looked like all the herbicide pictures. It seemed weird to me though because I used the same mulch on other potato beds that were doing just fine. I figured maybe certain varieties were more susceptible.
Eventually, I figured out the curly leaves were an early sign of pocket gophers munching the
roots. They tunnel in from far away, so you don't even realise they're there. It seems like the symptoms can be different depending on when during the life cycle if the plant the gophers get into the bed, what type of potato, etc. After a couple months though, I was certain that the curly leaves were from gopher damage
underground.