Place potatoes in a medium saucepan; add water to cover and, if desired, 1/4 teaspoon salt. Bring to boiling; reduce heat. Simmer, covered, for 15 to 20 minutes or until just tender. Drain well. Cool slightly. Cut potatoes into quarters and place in a large bowl.
Meanwhile, for dressing, in a small bowl combine mayonnaise, lemon juice, garlic, and pepper. Stir in olives, capers, green onion, and anchovies. Pour dressing over potatoes. Add onion and eggs. Toss gently to mix.
Cover and chill for at least 4 hours or up to 24 hours, stirring salad occasionally. Makes 6 side-dish servings.