In a 5-to 6-quart pan, bring about 2 quarts water to a boil over high heat; add potatoes. Cover and simmer over low heat until potatoes are tender when pierced, 15 to 20 minutes. Drain and chill.
Soak the onions about 15 minutes in cold water to cover. Drain and mix onions with rice vinegar. Cut potatoes in quarters; add to onions.
Trim tender watercress sprigs from stems, then finely chop enough of the course stems to make 1/2 cup (discard extras or save for other uses). Mix chopped stems on a large oval platter with potato salad alongside; cover and keep cool.
Rinse salmon and pat dry. Place, skin side down, on a piece of heavy foil.
Cut foil to follow outlines of fish, leaving a 1-inch border. Crimp edges of foil to fit up against edge of fish. Mix soy sauce with brown sugar and brush onto the salmon fillet.
Lay fish on center of grill, not over coals or flame. Cover barbecue (open vents for charcoal) and cook until fish is barely opaque in thickest part
(cut to test), 15 to 20 minutes. Transfer fish to platter with salad. Add salt to taste.Serve hot or cold.