To make scallion oil: Chop enough scallions (including greens) to measure about 1 1/4 cups and in a blender puree with oil and salt and pepper to taste until smooth. Pour puree through a fine sieve into a bowl, pressing hard on solids. Discard solids. Scallion oil may be made 1 day ahead and chilled, covered. Bring oil to room temperature before using.
In a large saucepan cover potatoes with salted cold water by 1-inch and simmer until just tender, about 7 minutes. In a colander drain potatoes and rinse under cold water to stop cooking. Pat potatoes dry. Potatoes may be prepared up to this point 1 day ahead and chilled, covered. Halve potatoes lengthwise. In a bowl, toss potatoes with 1 tablespoon olive oil and season with salt and pepper.
Peel and devein shrimp. Remove tough muscle from side of each scallop if necessary. Pat shellfish dry and in a bowl toss with remaining 2 tablespoons olive oil and salt and pepper to taste. Prepare grill.
Grill potatoes, cut sides down, on an oiled rack set 5 to 6 inches over glowing coals 1 to 2 minutes on each side, or until lightly charred. Grill shrimp and scallops 2 minutes on each side, or until just cooked through and golden brown. (Alternatively, saute potatoes and shellfish in a lightly oiled non-stick skillet in batches over moderately high heat.)
Spoon salsa onto centers of 6 plates and mound mesclun on top. Arrange shellfish and potatoes around salsa. Drizzle shellfish and potatoes with some scallion oil.
Finely chop shallots and mince garlic. In a bowl toss shallots and garlic with coriander. Discard husks from tomatillos and rinse tomatillos under warm water to remove stickiness. Chop tomatillos and add to shallot mixture, tossing to combine.
Peel and pit avocados and cut into 3/4-inch pieces. Add avocados to tomatillo mixture, gently tossing until just combined. Season with lime juice, salt, and pepper, to taste. Salsa may be made 4 hours ahead and chilled, its surface covered with plastic wrap.