Some actions I took in the game, and applicable COIN lessons.
1.) Despite the fact that I killed government forces and trained dozens of militia troops, I found that I still had to go on quests to help the oppressed people of the fictional nation in order to to gain valuable intelligence, get access to more weapons, or find caches of money. Granted, I spent much of that money at the whore house in the game, but I'd probably do that in real life too, if given the opportunity.
2.) The children of the local town were forced to work at a sweat shop, making clothing for a big-name celebrity. After liberating the town, I confronted the owner of the sweat shop. After my demands that she cease violating human rights were unsuccessful, I proceeded to shoot her. In front of the kids. The kiddies cheered, with one of them claiming that he wished he was old enough to shoot the bitch himself. Who knows, maybe there's a COIN lesson in this.
3.) The greatest concern for the local population was security. During combat, the scurry about, hoping not to be shot either by the government or by my insurgents. While the locals--save for a small, rich elite--had little love for the dictator, they needed some guarantee of security and success in order to trust my insurgent organization and aid the rebellion. Indeed, they were taking a great risk assisting me--should I fail, they would be labeled as collaborators and killed when my rebellion was crushed. Indeed, I needed to demonstrate to them that we were successful, and, by training local security forces, that I was here to stay.
4.) Even an all-powerful dictator has areas into which his or her power is minimal. In the game, there's a seedy city where the dictator has minimal presence. In Saddam-era Iraq, there was the Kurdistan region.