In a large nonstick frying pan, spread potatoes evenly. Add butter and 3/4 cup water. Cook over medium-high heat, partially covered, until water evaporates and potatoes are soft, 8 to 10 minutes. Uncover, reduce heat to medium, and cook, stirring occasionally, until potatoes just begin to turn golden on the edge, about 5 minutes. Season lightly with salt and pepper and keep warm over low heat.
Meanwhile, with a small, sharp knife, cut ends off orange and set on a cut side. Following the fruit's curve, slice off peel and white pith. Cut orange between inner membranes to release segments; discard membranes. Finely dice segments and put in a medium bowl. Stir in jicama, shallot, radishes, avocado, dill, and lemon juice. Season to taste with salt and pepper.
Heat a large, heavy frying pan (not nonstick) over high heat. Season scallops with salt and pepper. Swirl in oil and heat until just beginning to smoke. Sear scallops until browned, about 1 minute. Turn and sear until just cooked through, about 30 seconds more.
Divide potatoes among 4 wide, shallow bowls. Arrange 3 scallops in each bowl and spoon on some jicama and orange mixture. Top bowls with bits of dill.
*Any orange works in this dish, but the Cara Cara holds its shape especially well when diced.