Mistake one, not closing the border.
Mistake #2: Putzing around with the UN for over 6 months leading up to the invasion, which gave Saddam (and his Euro/Russian allies) all the time he needed to get his WMDs out of the upcoming war zone.
Mistake #3: Attempting to "win Islamic hearts and minds" by being ultra-sensitive while fighting the terrorist insurgency. (One example of many -- not killing Sadr immediately). Islamics understand the language of overwhelming, merciless force only, and perceive anything less than that as weakness. ....which of course just serves to encourage them.
Mistake #4: Making the assumption that giving Arabs/Muslims American-style liberty/Democracy would result in a more stable nation less hostile to American interests. We saw what happened when (so-called) Palestinians were given voting rights -- they immediately elected Hamas to power.
That is for sure.
And being clueless about Islam; thinking Islam was a religion of peace, and it had been hijacked by a few fanatics. - tom