Bring a large pot of water to a boil. Add 2 tablespoons salt and the red potatoes. Return to a boil. Reduce heat, and simmer until just tender, about 7 minutes. Remove potatoes using a slotted spoon. Return water to a boil. Add sweet potatoes, and simmer until just tender, 4 to 7 minutes. Drain. Gently toss red and sweet potatoes with oil and rosemary; season with salt and pepper. Refrigerate for 1 hour.
Heat grill to medium-high. Gently toss potatoes, and transfer to grill; reserve bowl with oil. Grill potatoes, turning occasionally, until charred and heated through, 6 to 7 minutes. Brush potatoes with oil from bowl.
Serving idea: Leftover potatoes tossed with canned tuna, fresh tomatoes, and olives make a great salad.