Funny, there's one single instance of float to the left which does the trick when changed to the right. I say funny as that is the first thing one would test, you would think.
Centering it is probably something really different.
And FY for anyone, the nice sliding does not work in IE where opening happens instantaneously. Also IE8 (and I guess lower) does not support the border-radius.
I actually had no idea about all the stuff that can be supported via CSS without a single image. Round borders, transitions, shadows, etc.
I'm not making a commercial for it, but I found really nice pure CSS menus on the site I mentioned in copyright few messages above.