Place potatoes in a large saucepan and cover with water. Bring to a boil. Reduce heat; cover and cook for 15-20 minutes or until tender. Drain. Cool; cut into cubes.
In a large bowl, combine potatoes with the cucumber, broccoli, celery and eggs. In a small bowl, combine remaining ingredients. Pour over salad and gently toss. Cover and chill 1 hour before serving. Store in refrigerator.