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:
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
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
$this->output('<a name="fb_share" type="bu..........................ript>');
Building an advanced theme is very easy, see instructions here:
Section: Creating an advanced theme....
For any questions please comment or ask again.