Place the potatoes into a large pot with enough water to cover. Bring to a boil, and cook until potatoes are tender, about 10 minutes. Add the green beans and wax beans during the last 2 minutes to blanch them. Drain, and rinse under cold water to stop the cooking. Cool before adding to the dressing.

In a large bowl, mix together the mayonnaise, mustard, celery, dill, salt, and pepper. Add the cooled potatoes and beans, and stir to coat. Refrigerate until ready to serve.