The authors examined the pervasiveness of three pieces of misinformation in the American public: that the United States has discovered WMD in Iraq, that evidence has been found showing that the Iraqi regime worked closely with al-Qaeda, and that world opinion favored America's decision to go to war. Support for the war was found to be highly correlated with the possession of false beliefs on these three matters—86 percent of those who believed all three supported the war, as did 78 percent of those who believed two, and 53 percent of those who believed just one. Among people who knew the truth on all three scores, just 23 percent supported the war. One key finding was that misinformation about the state of world opinion was the single strongest predictor of support for the war.
Update: Commenters add the fair point, worth noting, that we don't know what sorts of countervailing false beliefs war opponents held. Also worth pointing out is that we don't know which way causation runs here. There's a well known cognitive phenomenon called confirmation bias: We tend to notice information and form beliefs that confirm what we thought in the first place. So it's not necessarily that people who supported the war did so because they had false beliefs. It may rather be that people who took a strong position on the war either way are more likely to later form beliefs—justified and unjustified—that give them the comfort of "confirming" that they were right.