Charter of the United Nations
CHAPTER XV
THE SECRETARIAT
Article 97
The Secretariat shall comprise a Secretary-General and such staff as the Organization may require. The Secretary-General shall be appointed by the General Assembly upon the recommendation of the Security Council. He shall be the chief administrative officer of the Organization.
http://www.un.org/Overview/Charter/chapte15.html
I thought I had read a few more details, but I don't see them; however, they don't change the substance of what's here.
We should all be concerned, IMHO.
If nothing else, the fact that HC is a sitting US senator and possible pres candidate, would be in direct violation of the spirit if not the the letter of Article 100:
Article 100
1. In the performance of their duties the Secretary-General and the staff shall not seek or receive instructions from any government or from any other authority external to the Organization. They shall refrain from any action which might reflect on their position as international officials responsible only to the Organization.