It seems to me that one way to find the bad guys is follow the electrical power. Saddam and company seem to enjoy all the modern conveniences. When they turned off the power to Baghdad it seems to me that that guys in charge are not going to do without electrical power- they are going to have their own independent power sources. Now of course, some "normal folks" are also going to have independent power sources, but it seems that by looking for power sources in blackout out Baghdad should narrow the possible locations. Perhaps, some way of measuring magnetic fields could give you a map. They are also going to have heat waste- so some way to detect infrared.
Also another way of finding the bad guys, is that these special police operate like wolf packs- we need to find a way of tracking them back to their dens.
The next part is where is the top leadership- now, it's possible some or most don't even operate in Iraq. They could spend most of their time outside of Iraq and visit once in while in order to have face to face meetings. Another possiblity is they could spend a lot of their time underground- and this is similar to not being in the country- they occasionally come to the surface for face to face meetings. Or both. Or neither.
The other aspect is who really runs Iraq. How do we really know that Saddam is actually the guy in charge. Or, of course, whether Saddam is still living. It seems to me that this place is not being run by one guy- rather it's being run by an ideology (and Saddam doesn't seem smart enough to have or constructed an ideology). What is this ideology? It doesn't seem to be related the Islamic religion. Rather it's got a strong materialist streak to it & you got that Stalin worship thing going. I would guess that Saddam regime had very strong ties to the Old Soviet Union.
Of course this strong connection to USSR, shows how incompetent our CIA was in it's decison to back Iraq (in order to check the USSR). How strong this connection is today is unknown, but perhaps a bunch of ex-KGB are currently employed in Iraq. Now, we were once pretty scared of being "taken over" by Soviets spies- why would it be so strange to think that a country were actually taken over. Taken over but at same time keep Saddam as the ruler in name only. Or it could have been taken over before Saddam came to power (in this case Saddam would be part of the team, instead of merely being a puppet).
Anyways, just some thoughts.