https://extensions.gnome.org/ вот оф сайт дополнений для Gnome Shell
Там нет решения. Максимум, на что я мог бы рассчитывать, так это на поддержку GNOME 3.2.2.1, а у меня GNOME 3.4 ... Вот, как я понял, ответ на мой вопрос... Будем ждать, когда освоят поддержку 3.4.
I'm using GNOME 3. Why can't I install extensions?
Support for installing extensions from this website was first added in GNOME 3.2, so if you are using GNOME 3.0, you'll need to upgrade to a newer Linux distribution. You can check what version of GNOME is installed on your system using the "System Information" panel of "System Settings". If you are using GNOME 3.2 or newer and installation still doesn't work, check to make sure that the "GNOME Shell Integration" plugin is installed and enabled in your browser preferences.
If you are behind a proxy, make sure you have configured your proxy in both your browser's configuration dialog as well as GNOME's Network panel under System Settings. GNOME Shell Extensions needs both settings panels configured for the one-click installation to work.
Note: there were some bugs in the browser plugin shipped in some versions of GNOME 3.2 that prevent it from working properly under WebKit-based browsers like Epiphany and Chromium. GNOME Shell 3.2.2.1 has fixed these problems, so make sure you are using it.
Пользователь решил продолжить мысль 28 Апреля 2012, 17:28:41:
Так, в принципе, более-менее разобрался. Снес все конфиги и переустановил систему "с нуля". Потом установил Синаптик, а в нем - gnome-shell-extentions и gnome-shell-extentions-common, а также gnome-tweak-tool. Все и заработало, только без gnome-shell-extentions-weather.