The server delivers graphics, levels, ganis, gmaps, and scripts. I'm not sure how general player state is delivered to other players (it could be P2P, client-server, or mixed architecture). My impression from when I was developing in the past is that it's mixed. In that case, lag on the client could be derived from P2P connections.
Generally when working on efficiency though, you need something measurable (i.e. the performance benchmark), and then you implement a divide and conquer strategy throughout your debugging code (i.e. this is on a test server) to measure what creates the largest performance barrier. Sometimes it can be something that nobody has even thought of and hasn't happened in practice.
Also, when you have a high volume of users, that will uncover a lot of problems on its own (a testament from personal experience). However, that is often dependent on the user actually saying something, so kudos.