Start by quartering the potatoes and placing them in a large pot. Cover with cold water, bring to a boil, add salt, and cook until tender.
While the potatoes are cooking, prepare the dressing by combining mayonnaise, pickle relish, mustard, vinegar, celery seeds, paprika, salt, and pepper.
Drain the potatoes, peel if desired, and chop into chunks. In a large bowl, mix the potatoes with the dressing, then add eggs, celery, onions, and dill.
Garnish with extra dill and paprika, cover, and refrigerate for at least 4 hours. For best flavor, let it sit overnight. Serve chilled.