1. Combine first 3 ingredients in a large bowl. Add grapefruit, orange, and blood orange sections; toss gently.
2. Combine the shallots and next 6 ingredients (through pepper) in a small bowl, stirring well with a whisk. Drizzle dressing over salad; toss gently to coat. Divide salad evenly among 6 plates. Divide the pomegranate arils and toasted pistachios evenly among servings.