Bring a large pot of salted water to a boil. Add potatoes; cook until tender but still firm, about 15 minutes. Drain, and transfer to a large bowl.
Place eggs in a saucepan, and cover completely with cold water. Bring water to a boil. Cover, remove from heat, and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water, and cool. Peel, chop, and add to potatoes.
In a small bowl, combine lemon juice, oil, sugar, seasoned salt, Worcestershire sauce, mustard powder and black pepper; mix well. Blend in mayonnaise. Pour lemon dressing over potatoes, and stir to coat.
Mix in green onions, celery, and parsley. Refrigerate for at least 2 hours before serving.