Putting butter on a burn seals the heat in and causes the subdermal layer to continue cooking, causing worse and deeper burns. While it's a common old wives' tale, butter (or any greasy, fatty substance) is a bad idea for a burn for the same reason it's a good idea for cooking a turkey (which Stefanie Powers, being a vegetarian, would have no reason to know).
The villain's office is set in the same physical building as the villain's office in Does She or Doesn't She (1980), just two episodes earlier. In the first shot, you can see the corner of the building where the salon was set.