Hibernate is still not working :-( But I must admit that I have not pursued it much - Suspend works. I was more interested in getting Flash and Java running in Firefox. Having a 64bit Ubuntu is nice but it has a minor pitfall. There is a lack of important plugins for the 64bit version of FF.
I came across the following forum entry: http://ubuntuforums.org/showthread.php?t=202537
The offered script works great. It installs a 32bit version of Firefox, the Flash plugin etc.