Is it normal for potatoes to look like they are 'shedding'?
This is perfectly normal for waxy potatoes; their skins are soft and easily scraped off, especially if freshly harvested and handled roughly.   I saw it just the other day with a batch of new potatoes fresh from the CSA.  The potatoes were just fine. 

If you see this with thick-skinned, starchy potatoes it may be a sign of fungus, especially if accompanied by dried out or roughened patches.  Green colors in the peel are also a problem, because they indicate exposure to light and an elevated level of the toxin solanine. Solanine can cause upset digestion and headaches if consumed in quantity.  Don't eat potatoes that are very green.