To make roasted potatoes crisp, toss them after roasting. The tossing action will make the mushy parts crumble into a crispy exterior. You can skip using parchment paper or foil for roasting. If the potatoes tend to stick to the baking sheet, spray it with cooking spray. But the fat in the recipe will ensure that the potatoes do not stick. In addition, the potatoes will stay crisp for longer.