The UN lacks moral authority. It is no more moral than the member states that make up the organization. It is a failure. Ask the Hutus and Tutsis of Rwanda. Ask the Bosnians. Ask the people of Iraq what they thought of the UN during Saddam's reign.
The European position and many on the American left hold the view that only the UN has "moral authority". Herein lies the argument over what is moral. I would submit that when people speak of the UN having moral authority, they are referring to it being an institution of laws. Laws may constitute authority, but "moral" is a separate term and does not automatically follow having laws. The Taliban had quite a few laws in Afghanistan, most of them repressive, especially to women. Nazi Germany was defined by law but was an immoral government of the highest order. The Soviet Union had many laws, but there was no freedom of speech, action, religion or the right to own property.
The UN has squandered its legitimacy by allowing countries like Syria to be on the UN Human Rights Commission when the United States is voted off. The Oil-for-Food Scandal, the corruption that is rife within the organization and its focus on discussion without action is the existing legacy of the UN.
The United States, over time, should divest itself of the UN and its dominant role in paying for the UN's budget. In its place, the US should support the creation of a different collective security body with the right to join based on having a representative government with fair and free elections.
Only by freedom being the ticket to admission can a collective body have moral authority. The United States should, in all cases, pursue promoting freedom. Creating a coalition of the free is a good way of designing a new institution to do what the UN has proved incapable of doing, which is promoting security and human rights throughout the world.