Place potatoes in the bottom of a large pot and cover with water. Bring to a rolling boil over medium heat. Let cook for 20-30 minutes or until tender. Place potatoes in a colander and rinse with cold water. Let cool for 10-15 minutes. Peel and dice potatoes and place in a large mixing bowl. Add celery, onion, pickles, fresh dill, and salt and pepper. Set aside. In a medium mixing bowl, whisk together mayo, mustard, and vinegar. Pour dressing over warm potato mixture. Stirring until everything is coated well. Refrigerate until ready to serve.