Preheat the oven to 350°. Put the beets in a medium baking dish. Drizzle lightly with olive oil and rub to coat the beets. Cover with foil and bake for about 1 hour and 15 minutes, until the beets are tender. When the beets are cool enough to handle, peel and quarter them.
Meanwhile, in a small bowl, cover the onion slices with the vinegar. Add a large pinch of salt and mix well. Let stand for about 1 hour.
Using a sharp knife, peel the tangerines and grapefruit, removing all of the bitter white pith. Working over a bowl, cut in between the membranes to release the sections.
In a small bowl, whisk the mustard with 3 tablespoons of the vinegar from the onion slices. Whisk in the 1/4 cup of olive oil and season with salt and pepper.
Put the spinach in a large bowl. Drain the onion slices and add to the spinach along with the tangerine, grapefruit and beets. Drizzle the mustard dressing over the salad and toss well. Serve right away.