The most effective tool against terrorism
If you were to look at the events in the UN before the war in Iraq, they dont seem that important - either then or now. The US only went to the UN as a favour to Blair to cement his support for their invasion of Iraq, and France, Russia and China were never going to support a US war that would throw possibly the greatest oil reserves in the world solidy into the US sphere of influence. The US didnt get its UN approval, it predicatably went ahead anyway, and won easily. The lack of UN support wasnt important.
But it was. If you are fighting terrorism or guerilla groups you need legitimacy - you need to be able to demonstrate that you are the lawful authorities and the opposition are the crinimals. The lack of UN support isnt important in the Arab world because the UN is not much more loved there than the US. But it would be quite useful to have that support when youre trying to drum up support from other states for US efforts in Iraq. Iraqis might be glad to see the back of Saddam, but they dont view the US forces as the legitimate authorities there, no more than they view the guerilla groups there as legitimate anyway. They are after all, both foreign groups who probably hold their own interests closer to their hearts than the interests of the Iraqi people.
The last scrap of legitimacy the US could have claimed was the WMD claim which has been shown to be at the very least unproven - it was a poor choice to base the US case on, because it relied upon Saddams input, which they couldnt know, control or predict. If they had claimed they were going in to depose a evil dictator, to allow the ending of terrible UN sanctions, to end what was a practical military standoff since the Kuwait war, then they would enjoy at least that much legitimacy - both internationally and with the Iraqis.
Because of their lack of legitimacy the US is not going to be able to beat the guerillas there. Why should an Iraqi report that he overheard some guys talking about planting a mine on a Us convoy route? They best they can do is try and keep a lid on the situation until the Iraqi authorities are able to take up the security role and then try not to be heavy handed in their dealings with the Iraqi leaders - they will need to understand that the Iraqi leadership are going to have to do and say stuff to "prove" their not US lackeys, to gain legitmacy with the Iraqi people. On the other hand the Saudis are dealing far more successfully with their home grown terrorists, with the widespread support of the people there, because they are viewed as having a legitimate right to force, and people are more inclined to trust and work with them.
For another example - from Irish history - Dev used internment to arrest and hold indefinitly without trial any and all suspected IRA men during WW2, to prevent them carrying out sabotage against the British. This action broke the IRA in the south and was hugely successful in its aim.
In the 70s the British tried internment to break the IRA in the north - the policy failed disastrously, serving only to increase IRA recruitment and garner sympathy for their cause. The difference was legitimacy. DeValera had it, the British didnt.