Many mistakes were made. For example, the US official in charge of prisons decided to work with Ali al-Jabouri, the warden of Abu Ghraib prison, apparently unaware of the prison's fearsome reputation as the place where tens of thousands perished under Saddam Hussein. The coalition rehabilitated Abu Ghraib and today uses it as a prison. The symbolism may be lost on the US administrators but it is not lost on Iraqis.
It's worth reading in its entirety IMHO: How to Get Out of Iraq. It's especially relevant with regard to Torie's comment, BTW.
PS. This was written well before the whole prison abuse scandal broke into the open.
Which of the three states will Bagdad be in?
The biggest mistake was that we did not crush Iraq sufficiently in the original conflict. We didn't defeat Iraq's army we accomplished a coup d'etat by just entering Baghdad and saying 'here we are'.
The armchair generals say we should have kept the Iraqi army together, but we didn't disband their army they just melted back into the population.