Put the potatoes in a large saucepan, cover with water and bring to a boil. Add a large pinch of salt and simmer until the potatoes are tender, about 35 minutes. Let cool slightly, then peel the potatoes and cut them into 1-inch dice.
Meanwhile, in a bowl, combine the mayonnaise, mustard, onion, relish, dill pickle, parsley and celery seeds. Season with salt and pepper. Fold in the potatoes, celery and eggs and let cool; refrigerate until chilled and serve cold.