The problem is that the jQuery from the Blog component is interfering with the jQuery from the superfishmenu module. The jQuery from the module loads last and there are 2 problems:
1. It uses an old version of jQuery, 1.2.6
2. The jQuery UI functions are overwritten
To fix this issue, you'll have to copy some files and edit one file.
1. Copy the files:
[Joomla dir]/components/com_blogfactory/assets/js/jquery-1.3.2.min.js
and
[Joomla dir]/components/com_blogfactory/assets/js/jquery-ui-1.7.2.custom.min.js
to the folder:
[Joomla dir]/modules/mod_superfishmenu/tmpl/js/
2. Rename: [Joomla dir]/modules/mod_superfishmenu/tmpl/js/jquery.js to: [Joomla dir]/modules/mod_superfishmenu/tmpl/js/_jquery.js
3. Rename: [Joomla dir]/modules/mod_superfishmenu/tmpl/js/jquery-1.3.2.min.js to: [Joomla dir]/modules/mod_superfishmenu/tmpl/js/jquery.js
4. Edit [Joomla dir]/modules/mod_superfishmenu/helper.php and add on line 41
$addScripts[] = 'jquery-ui-1.7.2.custom.min';