Place the potatoes into a pot, and cover with water. Add the 2 teaspoons of salt, and bring to a boil.
Reduce the heat to low, and let the potatoes simmer until they are just fork-tender.
When the potatoes are cooked, drain them in a colander and let them cool for about 15 minutes.
While the potatoes are cooling, prepare the vegetables and eggs as directed above.
Mix together the mayonnaise, vinegar, mustard, dill, salt, and pepper.
Add the eggs, celery, and onions to the cooled potatoes, and pour the dressing over everything. Stir gently to combine everything.
Taste, and adjust seasoning as needed.
Chill the potato salad until ready to serve. Keep any leftovers refrigerated in a covered container for up to 4 days.