How to Make It
Preheat the oven to 350°. On a rimmed baking sheet, toss the red potatoes with 1 tablespoon of the olive oil and spread them in an even layer. Season with salt and pepper. Bake the potatoes in the middle of the oven for about 30 minutes, or until they'e lightly browned and just tender. Let cool.
On each of 2 large rimmed baking sheets, toss half of the sweet potatoes with 2 tablespoons of the olive oil. Spread the sweet potatoes in an even layer and season with salt and pepper. Bake the potatoes on the upper and lower racks of the oven for about 20 minutes, or until lightly browned and just tender; switch the sheets halfway through for even cooking. Let the sweet potatoes cool.
In a large skillet, toast the mustard seeds over moderately high heat until they start popping, about 3 minutes. Transfer the seeds to a small bowl. Add the rinsed spinach leaves—they will still be wet—to the skillet and cook over moderately high heat, tossing with tongs, until completely wilted. Transfer the spinach to a colander to cool. Lightly squeeze the spinach dry and then coarsely chop.
Wipe out the skillet. Add 2 tablespoons of olive oil and heat until shimmering. Add the okra, season with salt and pepper and cook over moderate heat, turning a few times, until the okra is lightly browned, about 5 minutes.
In a very large bowl, mix the vinegar with the capers and the remaining 1/4 cup plus 2 tablespoons of olive oil; season with salt and pepper. Add the red potatoes, sweet potatoes, mustard seeds, spinach and okra and toss well to coat. Transfer the salad to a platter and serve.