The world best trained, best equipped military is unable to quell the insurgency in Iraq. The lesson here is the standard one of the nature of asymetric warfare. But, let's look one step deeper at the role the American military is trying to fulfill ... with a thought experiment.
Imagine swapping the entire police force of New York City with that of Tokyo, Japan. Just move all of them on 747's overnight and trade homes and jobs. There may well be some New York policemen who can speak some Japanese, but most would not know a single word. Both police forces, though professional and well trained could not be effective in policing each other's cities.
There is just too much they don't know about the culture, even beyond language. Imagine a Tokyo policemen trying to solve a crime without understanding concepts such as "gang banger" and "drive by" and having to accomplish all the work through a translator. Where do criminals congregate? What does "normal" behavior look like?
The American military has one other disadvantage: they are not trained for law enforcement (except for the military police). Their training is in defeating enemy soldiers, not solving crimes and providing security.
The job is impossible. Period. Get them out of there. We need a strong military to do what they can do. Not this.