Scrub and peel potatoes. (You can leave some of the skins on if you like the texture.) Chop into roughly 1" cubes and transfer to a stockpot.
Add enough cold water to cover the potatoes by 1 inch, and heat over medium-high until boiling. Add in 1 tablespoon of salt. Reduce heat to medium-low, cover and simmer until tender (about 8-10, minutes depending on how small you chopped the potatoes). To know they're done, you should be easy to pierce with a fork, but still hold their shape.
Drain potatoes and transfer to a large bowl to cool slightly.
In the meantime, make the dressing. Whisk together the vinegar, lemon juice, mustard, and olive oil with the dill, parsley, green onions and garlic.
Pour the dressing over the slightly cooled potatoes. Add the celery, and toss to coat. Adjust salt and pepper to preference. You can serve it warm immediately, or cover and chill until time to serve. This can be made a day in advance.