There are a lot of tweaks that need to be made.
One thing is that you should be using menu_black.png instead of menu_white.png since your page background is white.
Another big issue is that you have .content set with a width on line 50 of your main.css file. You need to override this in your responsive.css file so that if the page is small it doesn't force that area to be so wide.
I'd also suggest hiding the sidebar in the responsive.css so that it doesn't show on mobile at all since they can use the top menu.
I think you can work through all of the issues on this page, but you can start over too... I guess that is up to you.