Place peeled and cubed potatoes in large saucepan and add water to cover by 1 inch. Bring to boil over medium-high heat; add 1 tablespoon salt, reduce heat to medium, and simmer, stirring once or twice, until potatoes are tender, about 8 minutes.
Drain potatoes and transfer to large bowl. Add vinegar and, using rubber spatula, toss gently to combine. Let stand until potatoes are just warm, about 20 minutes.
In a separate small bowl, mix together celery, onion, pickle relish, mayonnaise, mustard powder, celery seed, herbs, pepper, and 1/2 teaspoon salt. Toss this with the potatoes and chopped eggs. Cover and refrigerate until you are ready to serve.