First off, you can remove all the "background-color: inherit;" values. Everything is automatically inherited anyway, hence the "Cascading" part of CSS.

For the IE problem, you don't need to use the position property in this situation. Merely floating the content to the right and the navigation to the left will work.

And for the FF issue: Instead of .menu, use .menu a and .menu a:hover. This is most likely the culprit.