Preheat oven to 350 degrees F. Cook pasta according to package directions; drain. Meanwhile, remove chicken from bones, discarding skin and bones. Using two forks, coarsely shred chicken.
In a medium saucepan, melt butter over medium heat. Stir in flour. Gradually stir in broth. Cook and stir until thickened and bubbly. Stir in capers, the 2 tablespoons dill, mustard, lemon peel, lemon juice, salt, and pepper.
In a large bowl, combine cooked pasta, shredded chicken, dill mixture, squash, sweet pepper, and onion. Transfer mixture to an ungreased 3-quart baking dish.
Bake, covered, about 35 minutes or until heated through. Sprinkle with pine nuts and garnish with additional fresh dill. Makes 6 to 8 servings.