There's a good article here.. It sounds like there probably is quite a bit of oil, but Iraq has been in a long series of wars and revolutions so the place is rarely stable enough to try and develop it.
No doubt Iraqi oil production is in a very bad shape, needs investments and could be somewhat higher. Exploding pipelines are not good for oil exports. These thing happen in a war. But otherwise there is this usual talk about increasing capacity a lot in the future. Practically every oil producing country talks optimistically about increasing capacity. They don't like to admit being in decline. It has been very difficult for the UK, even for the US. Countries in decline like insted to talk about the need for huge new investments.

My point was the apparent lack of interest in Iraqi oil. From the article of al-Chalabi we see that capacity increase would come from applying new technology to the mostly old, quite mature fields and repairing the ailing infrastructure. This is not possible during the war, and don't promise easy profits in any case.

The reality is that while experts complain about the possible permamenent destruction of existing capacity by mismanagement and lack of maintenance, nothing is done. It is widely acknowledged now that the war is unwinnable for the US and would continue indefinitely despite of the present political process. The get the Iraqi oil fully online something else would be needed. But obviously the Iraqi oil is not interesting enough to change the course.  

There are a bunch of large and medium undeveloped fields: Majnoon, Nahr 'Umar, West Qurna, Halfaiya, East Baghdad, Ratawi, Nasiriya, Khormala, Hamrin, and Gharraf . If you go Google these fields, you'll find details of past development plans for them that have been shelved, and you'll see that getting to 5-6mbpd is not at all unrealistic if the place could be stabilized, and there probably are somewhere in the general range of 50-100 billion barrels or recoverable reserves in the known fields. I very much doubt it will be stable anytime soon.

Here are some links:

The last is particularly interesting.