Didn't you hear? Once we used it to dethrone MSIE, we realized that we didn't actually give a shit about compatibility. It was just the best stick we had to beat IE with.
atm we are only supporting the latest browser versions to speed up development but if there's enough interest in supporting other versions we're happy to do so
After looking at your CSS, I believe the only issue is that you don't appear to be defining how the newer HTML5 elements should be displayed. It's common to simply put display: block, or inline-block, for all of the HTML5 element that you're using. This should fix the garbled mess that you see in the screenshot. I don't believe that there is much more to it than that. Although, I do not have the version of Firefox mentioned to test on.