Unfortunately, there are still some bugs with the application for Android tablets.  You are able to download the application from the Google Play Store but with the shortcut that gets created there is a problem with it.  This is where the issues lie.

To correct this, you can launch Handheld Contact from the Applications list.  From there, HHC should open successfully.  Since the shortcut is corrupt, you can delete it from the home screen and create a new shortcut from the Applications list.

Once Handheld Contact is launched on the tablet, the Contact List is only viewable in Portrait mode.  The rest of the options (Task List/Calendar) will be available in both Portrait and Landscape modes.  This will be something changed in HHC in a future build.

UPDATE:  These bugs for Android tablets have been resolved.  Please upgrade to the most recent application to utilize Handheld Contact.  Click HERE for more info.