Mix masa, salt, soda, potato, and cheese. Shape into balls the size of an egg. Place, one at a time, between two sheets of waxed paper and flatten with a rolling pin or tortilla press to 4 or 5 inches in diameter, or ¼ inch thick, whichever you arrive at first. Make these ahead and cover with a damp paper towel.
Heat 1 inch of oil in a small skillet and fry each patty 5 minutes on each side and drain on paper towels.
To garnish, cover each patty with hot Salsa de Chile Colorado and top with olives, onion, and cheese. Mix the vinegar and dried oregano in a small bowl and serve on the side with a bowl of shredded lettuce or cabbage.