It seems that the primary flaw of the United Nations could be the lack of an enforcement mechanism. Outside of public reprimand, the consequences a United Nations ire is fairly minimal. Nations can quickly flout such judgments and assessments from the governing body. Another primary criticism of the United Nations is the role of the United States. Some feel that the UN is merely an instrument or extension of the United States and their attempt to mold world opinion into their own international aims. In my mind, I would say that these two areas represent two significant arguments regarding the ineffectiveness of the United Nations.
The major criticisms of the UN and of any other international, collective security body are that A) it has no power to make anyone obey its commands and B) it has no real will to make hard decisions because its members cannot agree on anything.
If you look at the issue going on with Iran and its nuclear weapons, you can see how this would be. The UN has told Iran over and over to stop with its nuclear program. Iran pretty much just refuses and does what it wants. The UN cannot get really tough on Iran because Russia and especially China do not really want to punish Iran.
So the UN is too wishy-washy to make a decision and too weak to enforce any decision it does make.