What you're trying to do is a tough row to hoe, but I'll give you some general suggestions:
1 - overall the entire design needs some padding, especially on the left hand menu
2 - The liquidity of the design is having some issues when you shrink your browser window down. Funky wrapping and non-desired behavior in the header
3 - Make the menu items on the left side links. That's what they do, that's what they should do.
In general, your markup needs some work -- you're using div and p tags all over the place, when those aren't really the best way to represent your data. Also, I see a lot of places where you're using classes that would be better served by ids.
Making your markup semantic and valid will go a long way towards addressing cross-browser issues. Especially on a site like this, where pixel-perfect reproduction isn't important, but you do want the site to look good and be usable across all browsers.
Shoot me a PM if you want any more specific suggestions - it seems like you have the desire to "get it right", so I might be able to offer some experience + advice.