The plugin fails to install when WordPress is installed in a subdirectory (e.g. http://www.example.com/wp) but accessed via the root (www.example.com).
Line 86 in wp-social-login.php appears to be the culprit. Replacing
require_once( dirname( dirname( dirname( dirname( __FILE__ )))) . '/wp-load.php' );
require_once( ABSPATH . '/wp-load.php' );
Allows the plugin to install. If this is a valid fix, I'd appreciate it if you could include it in a new release as we'd like to include the plugin via svn:externals without third party edits. If this has any unintended consequences I'd happily work with you to resolve them.
Edit: The problem also exists on authenticate.php, line 37 - although this will have to be resolved in a different way.