You actually can add a Like It button to each question through the advanced theme. See here or, if You need more detailled explanation comment again:
http://highedwebtech.com/2010/04/22/how-to-add-facebooks-like-button-to-any-page-on-your-site/
Here You have a sample on my site:
http://www.yourquestionplease.com
Just click on one question and see. You may try it as often as You want.
EDIT: I changed the site and included the Share Button instead of the like button. It is very easy as well.
the advantage is, that a liked item in facebook shows up as a small announcement, and a shared item shows up with picture and comment as long as the sharer provides one.
To make this available in Your installation go to
http://www.facebook.com/share/
Copy the code and add it in Your advanced theme to the function and place You want.
In the case of my site it is in the function
function q_view_main($q_view)
{
$this->output('<DIV CLASS="qa-q-view-main">');
$this->q_view_content($q_view);
$this->output('<a name="fb_share" type="bu..........................ript>');
..............
Building an advanced theme is very easy, see instructions here:
http://www.question2answer.org/advanced.php
Section: Creating an advanced theme....
For any questions please comment or ask again.