Has there been a WWIII since the UN has been in power? No.

Well that is its primary purpose.

Let's just make this simple. If the U.S wants to do anything, it can do what it wants. If other nations want to do something unorthodox, then they really have to square it with America if they don't want any sanctions. If the U.S wants to impose sanctions on a country, it can. The power of the U.S is its economic power. The threat of denying a country the American market is enough for them to vote for U.S policy. America is the enforcer of the U.N.
Subsitute China in there and you will see why it is getting away with Tibet and bullying Taiwan...

Subsitute France in there and you will understand why it got away with the Nuclear Tests in the South Pacific and France getting the so much benefit from the CAP.

Subsitute Britain in there and you are left perplexed.