With Peter's fix I have the following:

➜  ~  software-center
2013-03-06 13:18:22,757 - softwarecenter.ui.gtk3.app - INFO - setting up proxy 'None'
2013-03-06 13:18:22,763 - softwarecenter.db.database - INFO - open() database: path=None use_axi=True use_agent=True
2013-03-06 13:18:23,208 - softwarecenter.backend.reviews - WARNING - Could not get usefulness from server, no username in config file
2013-03-06 13:18:23,316 - softwarecenter.ui.gtk3.app - INFO - show_available_packages: search_text is '', app is None.
2013-03-06 13:18:23,328 - softwarecenter.db.pkginfo_impl.aptcache - INFO - aptcache.open()
2013-03-06 13:18:24,134 - softwarecenter.db.categories - WARNING - '/usr/share/desktop-directories/Utility.directory' has no name
2013-03-06 13:18:24,135 - softwarecenter.db.categories - WARNING - '/usr/share/desktop-directories/Utility-Accessibility.directory' has no name
2013-03-06 13:18:24,141 - softwarecenter.db.categories - WARNING - '/usr/share/desktop-directories/Education.directory' has no name
Traceback (most recent call last):
  File "/usr/bin/software-center", line 182, in <module>
    app.run(args)
  File "/usr/share/software-center/softwarecenter/ui/gtk3/app.py", line 1387, in run
    self.show_available_packages(args)
  File "/usr/share/software-center/softwarecenter/ui/gtk3/app.py", line 1325, in show_available_packages
    self.view_manager.set_active_view(ViewPages.AVAILABLE)
  File "/usr/share/software-center/softwarecenter/ui/gtk3/session/viewmanager.py", line 151, in set_active_view
    view_widget.init_view()
  File "/usr/share/software-center/softwarecenter/ui/gtk3/panes/availablepane.py", line 139, in init_view
    SoftwarePane.init_view(self)
  File "/usr/share/software-center/softwarecenter/ui/gtk3/panes/softwarepane.py", line 138, in init_view
    self.icons, self.show_ratings)
  File "/usr/share/software-center/softwarecenter/ui/gtk3/views/appview.py", line 70, in __init__
    self.helper = AppPropertiesHelper(db, cache, icons)
  File "/usr/share/software-center/softwarecenter/ui/gtk3/models/appstore2.py", line 108, in __init__
    self.all_categories = cat_parser.parse_applications_menu()
  File "/usr/share/software-center/softwarecenter/db/categories.py", line 277, in parse_applications_menu
    category = self._parse_menu_tag(child)
  File "/usr/share/software-center/softwarecenter/db/categories.py", line 471, in _parse_menu_tag
    query = self._parse_include_tag(element)
  File "/usr/share/software-center/softwarecenter/db/categories.py", line 429, in _parse_include_tag
    xapian.Query.OP_AND)
  File "/usr/share/software-center/softwarecenter/db/categories.py", line 366, in _parse_and_or_not_tag
    operator_elem, xapian.Query(), xapian.Query.OP_OR)
  File "/usr/share/software-center/softwarecenter/db/categories.py", line 412, in _parse_and_or_not_tag
    q = self.db.xapian_parser.parse_query(s,
  File "/usr/share/software-center/softwarecenter/db/database.py", line 185, in xapian_parser
    xapian_parser = self._get_new_xapian_parser()
  File "/usr/share/software-center/softwarecenter/db/database.py", line 211, in _get_new_xapian_parser
    xapian_parser.set_database(self.xapiandb)
  File "/usr/share/software-center/softwarecenter/db/database.py", line 177, in xapiandb
    self._db_per_thread[thread_name] = self._get_new_xapiandb()
  File "/usr/share/software-center/softwarecenter/db/database.py", line 190, in _get_new_xapiandb
    xapiandb = xapian.Database(self._db_pathname)
  File "/usr/lib/python2.7/dist-packages/xapian/__init__.py", line 3666, in __init__
    _xapian.Database_swiginit(self,_xapian.new_Database(*args))
xapian.DatabaseOpeningError: Couldn't stat '/var/cache/software-center/xapian' (No existe el archivo o el directorio)