The report cited one example in which for nearly $4.5m a year, the state department assigned a 16-person security detail to protect six US contractors in Iraq who already had a team of hired guards they did not really need.
The incident is one of many described in the audit whose findings also suggest that the department remains ill-equipped to watch over the vast amount of US money still flowing into Afghanistan.
In a letter released along with the report, David Johnson, a state department official, disputed the audit's central conclusion that the contract, awarded in 2004, was vulnerable to waste and fraud.
Describing the audit's key points as "unfounded," Johnson said that payments were only made to a contractor after invoices have been carefully checked.
But the report challenged that assertion, saying that for the few years of the arrangement, the department had a single contracting officer in Iraq to monitor invoices to ensure the government got what it was paying for.
Overwhelmed by the volume and complexity of the paperwork, the lone officer was approving all DynCorp invoices without questioning them.
That means there is "no confidence in the accuracy of payments of more than $1bn to DynCorp" during the early stages of the contract, the report said.
There are now three contracting officers in Iraq overseeing the work, but the audit said that this was still too few and that these officers also needed more guidance on how to do the job.
US forces have been in Iraq since the US-led 2003 invasion to topple Saddam Hussein, the then-president.
Training Iraqi security forces, including police, has been an important element of US reconstruction efforts in the country and security responsibilities have gradually been returned to Iraqis.
Bowen said the contract awarded to DynCorp, which is headquartered in Falls Church, Virginia, was the largest ever managed by the state department.
The report did not judge whether or not DynCorp's training of Iraqi police had been a success or a failure.