In a medium saucepan place potatoes, the 1/4 teaspoon salt, and enough water to cover. Bring to boiling; reduce heat. Simmer, covered, for 15 to 20 minutes or until just tender. Drain well; cool slightly.
Meanwhile, for dressing, in a large bowl combine mayonnaise, mustard, the 1/2 teaspoon salt, and the pepper. Stir in the celery, onion, and pickles. Add the potatoes and eggs. Toss lightly to coat. Cover and chill for at least 6 hours or up to 24 hours.