Yes, in fact, I always do eat the skin. All the vitamins are right under the skin. I scrub the potato and cut out any brown spots and cook it and eat it all. Be sure to wash anything that grows above ground that isn't protected by thick skin. I wash apples every time and zucchini and yellow squash.
I LOVE potatoe skins. Take a couple of potatoes, wash them, wrap them in paper towels, put in microwave for about 8 minutes for each potatoe. When done slit them lengthwise, stuff in butter and sour cream or yogurt, sprinkle on chives, and pepper, mash the insides with a fork, and eat!