Using a food processor fitted with a coarse grating disk, grate the potatoes and onion; discard any large pieces. Transfer the mixture to a clean dish towel and squeeze out any excess liquid, then transfer to a large bowl. Stir in the flour, egg, 3/4 tsp. salt, 1/4 tsp. pepper and the baking powder.
In medium saucepan, boil 1 1/2 cups fresh cranberries, 3/4 cup sugar and 1/2 cup water, stirring. Lower heat and simmer until cranberries soften and burst, 10 minutes; let cool. To food processor, add 1 medium peeled, cored and quartered apple with sweet potato and onion. Add 1/4 tsp. freshly grated nutmeg to batter.
In a medium skillet, heat 1/4 inch oil over medium-high heat until hot but not smoking. Working in 5 to 6 batches, drop 2 tbsp. scoops of batter into the pan about 2 inches apart. Using a spatula, flatten the batter into disks. Cook, turning once, until browned and crisp, about 5 minutes. (Lower the heat if the latkes darken too quickly.) Drain on paper towels. Serve with cranberry sauce.