1) Roast potatoes and okra:
Put oven rack in middle position and preheat oven to 450°F.
2) Halve potatoes lengthwise and toss with scallion pieces, rosemary sprigs, 2 tablespoons olive oil, 3/4 teaspoon salt, and 1/2 teaspoon pepper. Spread potato mixture in a large roasting pan and roast, stirring once, 20 minutes. Stir potatoes and add red okra to pan, tossing to coat. Continue to roast until okra and potatoes are tender, about 30 minutes more.
3) Cook beans and corn while potatoes roast:
Cook beans in 1 quart (unsalted) boiling water in a 3- to 4-quart pot 3 minutes, then immediately transfer to a bowl of ice and cold water to stop cooking. Gently peel off skins.
4) Return water to a boil and add 1 teaspoon salt, then cook corn until tender, about 4 minutes. Drain corn in a sieve and immediately transfer to bowl of ice and cold water to stop cooking. Drain corn again.
5) Make dressing and assemble salad:
Whisk together lemon juice, shallot, chopped rosemary, and remaining 2 tablespoons oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper in a large bowl until combined. Discard rosemary sprigs, then add hot potatoes and okra to dressing along with beans, corn, and salt to taste, tossing to combine. Cool salad to warm before serving.