In order to run Hulu Desktop for Linux on a 64-bit system, you'll need the prerelease version of Flash Player for Linux 64-bit. Installing it requires the removal of the nsplugin and flashplugin-nonfree plug-ins which you're probably already using with Firefox. This can be done in System → Administration → Synaptic Package Manager in Ubuntu.
The download provides libflashplayer.so. You should create a new folder in your home folder under .mozilla named "plugins" and place the extracted file there.
If that was Greek to you, here's what to do. Download the tarball "libflashplayer-10.0.32.18.linux-x86_64.so.tar.gz" from the page above to your desktop. Once it's saved there, right-click the file and select "Extract Here."
Under "Places" in the Ubuntu main system menu, select "Home Folder." Under "View" in the File Browser, select "Show Hidden Files." Then scroll down and open the folder named .mozilla (note the dot). In this folder, right-click and select "Create Folder." Name the folder "plugins" and then open it.
Drag the libflashplayer.so file from your desktop into this folder.
And that's it. Hulu Desktop will be able to find it there.