Bring a large pot of water to a boil over high heat. Add shrimp, scallops, and calamari. Cover, remove from heat, and let steep just until shrimp are pink on the outside and opaque but still moist-looking in center of thickest part (cut to test), about 3 minutes. Drain seafood and immerse in ice water until cold; drain again.
Meanwhile, combine mayonnaise, lemon peel and juice, tarragon, mustard, and 1/2 tsp. each salt and pepper in a food processor. Whirl until smooth.
Combine seafood, watercress, capers, and dressing in a large bowl. Add more salt and pepper to taste. Gently stir in avocado.
Serve on a bed of butter lettuce or as a sandwich in thick, toasted bread.