A couple of things:
-Succession
Maybe there should be some leadership/heart/charisma/juice check to keep people when a leader dies, representing the damage to the organization.
-Jobs and sleepers
I don't like the ability for sleeps to work for you on their days off. They should have no contact with you at all. Instead of assigning LCS members to jobs, have them be able to try to become a sleeper, this check should be fallible. Sleepers should go stale at some point, no one maintains cover for 30 years without contact. Give players some sense of the mental state of the sleeper and an option to extract them from normal society. Perhaps working as a sleeper should even increase wisdom over the long run, leading to people turning on you.
-Seduction
Right now it seems like sleeping with someone can only be used to recruit, why not but a couple more options in there? The "love slave" could get guns, maps, documents, clothing or money for you. Downside is that the seducer need to spend time with them, or they go to the police.
-Other groups
I don't think the game should be tracking outside groups, after all the LCS is supposed to be so radical they have no qualms about killing a janitor because they "look" conservative. Everyone should appear to uninvolved to you. However, This does not mean that outside events shouldn't occur, just that they shouldn't be tied to any groups. Events like wars, recessions, protests, strikes, police crackdowns, elections, important court cases and contracts would still be really frickin' cool. That being said, it would be cool if you could buy into other organizations networks, like the KGB or Greenpeace. In exchange for cash, people or the occasional large job (think the weathermen's prison break) you should get access to a)info b)training facilities offsite (think becca valley) c) resources (additional safe houses, vehicles, equipment, cash). Of course this comes with a downside as well, if you cross your allies or attract too much heat they could turn on you.
-Fight club style recruiting
I really like this idea, but I want it further. As LCS become more widely know and more liked you should get recruits, and police informants. There should be some process for indoctrinating these recruits and bringing them into the LCS, while weeding out the moles. Roll recruitment up into interrogation, rename it indoctrination or something, and use the same interface for both. The only difference between a hostage and a recruit should be that the recruit wants to be there.