We recommend buying “dry” scallops, which don't have chemical additives and taste better than “wet.” Dry scallops will look ivory or pinkish; wet scallops are bright white.
Grate ½ teaspoon zest from 1 orange; set aside. Cut away peel and pith from oranges and grapefruit. Holding fruit over bowl, use paring knife to slice between membranes to release segments; set aside.
Pat scallops dry with paper towels. Heat 1 tablespoon oil in 12-inch nonstick skillet over high heat until just smoking, about 2 minutes. Sprinkle scallops all over with ¾ teaspoon salt. Add half of scallops, flat side down, in single layer around circumference of skillet; cook until browned, about 2 minutes per side. Transfer scallops to plate and tent with foil. Repeat with 1 tablespoon oil and remaining scallops.
Whisk shallot, vinegar, mustard, tarragon, orange zest, remaining ¼ cup oil, and remaining ¼ teaspoon salt together in large bowl. Add arugula and toss to coat. Add avocados, oranges, and grapefruit and toss gently to combine. Serve scallops over individual portions of salad.
