It is safe to reheat baked potatoes if they are stored correctly after they are cooked, according to the extension service at Penn State. Leaving a baked potato out on the counter at room temperature for an extended time sometimes leads to the growth of botulism, especially if the potato is left in a wrapper of aluminum foil.
Refrigerate baked potatoes after they are cooked. The leftovers are often dry, so they taste best when they are reconstituted in another dish. The leftover baked potatoes work well as an ingredient in a soup, as fried potato patties or mashed and mixed with milk and butter to top a casserole, such as shepherd's pie.