No need to be sorry, I think this is a very interesting topic. Obviously the majority of the suggestions contradict each other, and there are counterpoints to most ideas, but that's okay, it's good to explore and get a feel for the pros and cons of different directions.
One of the things Toady had listed on the to-do list for LCS is having a more robust list of issues and laws, noting that LCS doesn't even cover everything on the ACLU website. Off hand, Disability Rights, Drug Policy, HIV/AIDS, Immigrants' Rights, National Security, Racial Justice, Religion & Belief...
Expanding the Liberal Agenda screen wouldn't be too hard, it'll probably have similar code to the current poll screen where you can page through the issues. But another game issue that people have mentioned is targeting specific issues more effectively. Right now, every site is arranged with a collection of issues it affects. This works pretty well for shooting up the police station or pressing the big red button at the nuclear plant, but it's not obvious where gay rights or abortion fits. The answer is the courthouse right now for both, but the point is that it doesn't feel like you can target issues very easily.
So one question I have is how would you like to see being able to target specific issues? To give an example of an idea for how to enable more focus on specific issues, you could have the LCS be able to pick a set of issues that are emphasized especially heavily, and have your actions be more effective on these issues. Activism, the Guardian, writing to papers would also focus on these issues. Perhaps the longer the LCS emphasizes the issue consistently the more experience and credibility you build with it, thus further increasing your power with the issue, a mechanic that you can see in play in the President Forever games.
That's just an example I'm throwing out though, and I'd like to hear other ideas too.