What happens is the studs shrink behind the wallboard leaving a gap and then the wallboard is pushed in or pulled in by other screws or nails, the ones with the gap pop through. They are evenly spaced because the wall is screwed in every 8 inches or so.

You can fix them. Pick off the plaster covering them and if they are screws, screw them in tight. If they are nails hit them in tight. You don't want to sink them so deep that the cut through the top layer of paper on the wallboard, but you want them in a dimple that will hold the joint compound which will hid them.

Apply one or more coats of joint compound. You can buy it in small ready mixed cans. Sand with medium sand paper wrapped around a block of wood in between coats. Sand it flush and flat with the surrounding wall. Prime and repaint that area.