In a medium saucepan, cover the potatoes with cold water. Add salt, and bring to a boil. Cook until tender, about 15 minutes. Drain.
Bring a saucepan of salted water to a boil. Add the broccoli rabe, and cook until just tender; it should be bright green. Drain well, and cut into 5cm lengths.
Combine the oil, anchovies, and garlic in a large, deep skillet. Cook over high heat, mashing the anchovies, for about 1 minute. Spread the mussels in the skillet, top with the potatoes, broccoli rabe, and chopped parsley. Add 1/2 cup water, and season with salt. Cover, and cook until mussels are open. Serve.