This is all natural and nothing to worry about. You should after you dug them up. Leave them on top of soil for 30-1 hour, so the skins can dry out.
Potatoes form on an underground stem from the plants main stem, think of lots arms with a potato attached. The seed potato which you describe as " the base of the green stem is discoloured and has nothing on it ". Well yeah, the seed potato was only needed to grow the plant. The potatoes produced don't grow from this part of the plant.
Again, everything sounds fine to me, a part from perhaps a small crop, which sometimes happens.