According to the film maker, what we saw was in more respects not completely accurate. Some freedom was exercised while portraying the situation in Baghdad at that time. The existence of stand-in's, however, was realistic and publicly known. That went as far as showing them openly, if only to confuse potential attackers. It certainly reduced the risk in public appearances, since one could never know whether you saw the real one, or a double dressed and acting like the real one.
There were also questions about using English as the prime language. The producer had some arguments in favor of the choices made. Firstly, raising a 50M budget for a movie with Arabic speaking actors, was considered a Mission Impossible. Also, English is generally accepted as the standard movie language, spoken by Roman emperors as well as aliens from other planets.
The Q&A also revealed some facts about how Dominic Cooper handled his double role. We now know that he played both roles on the same day, given the entourage and colleague actors present that day. He always played the "lunatic" parts first, and (without much time in between) the "Latif" parts shortly after that. Of course, there was a challenge in keeping track of the places where the counterpart actor stood at particular moments during the scene. Anyway, if he missed a few and looked in a wrong direction at some instances, I did not notice it and I think the same of other people seeing this film for the first time.
At various moments throughout the screening the notion crossed my mind that this movie could be construed as a justification of overturning the Sadam regime, or (in other words) as propaganda in favor of George W for a completed project in Iraq. In retrospect, I don't think such a hidden meaning was intended. The film was not against Sadam as a dictator in particular, but rather against dictators in general. They existed and ruled since the time of the Roman emperors (and probably before that), and still are ruling nowadays in countries all over the world. We see the wrong side effects of unlimited power. We also see how uncooperative people were regarded "that is the thanks we get for uplifting this country" (or variations thereof).
Political issues and hidden meanings set aside, we saw a well constructed story line, believable casting, and an inside view in the palace and its inhabitants at that time. One can argue about the torture, punishment and other violent scenes, that these better could be left out, or otherwise included implicitly by telling about it (without showing actual pictures). On the other hand, leaving these out would change the film too much into a costume drama, thereby reducing the impact it now will have on the average viewer. Anyway, it is easy for us to criticize choices being made by the film makers. In my opinion they did their job very well, all things considered.