Can the UN serve as a balance against US dominance?
US power cannot be easily checked especially after the fall of USSR. Also, within UN the influence of US is considerable (single largest contributor to UN). Added to the fact that UN is located within the US territory. The power of US, veto power, considerable degree of say in choice of Secretary General are other points.
The UN is not therefore a balance to US. It can and has brought different countries and US together for discussion. Not that rest of world totally is against US, UN does provide space to put arguments against specific US attitudes and policies.
The UN is imperfect body but without it the world would be worse of.