the solution is quiet simple - just edit the wp-content/plugins/facebook-like-box-widget/facebook-like-box-widget.php file, and change the first line that start's with $like_box_xfbml to look like this:
"$like_box_xfbml = "<script src=\"http://connect.facebook.net/en_US/all.js#xfbml=1\"></script><fb:like-box href=\"$pageURL\" connections=\"$connection\" width=\"$width\" height=\"$height\" show_faces=\"$showFaces\" border_color=\"$borderColor\" stream=\"$streams\" header=\"$header\"></fb:like-box>";"
As you can see, it adds some parameters to the whole line, so it passes the height and connection parameters to the facebook script. It should work perfectly.
Although, one more thing. After you change this line, you should be able to adjust the height of the box through your widget configuration options. You must do it manually - change the height so it would fit your webpage template, and change the connection attribute to adjust how many faces you wanna see in your box. It won't adjust automatically.
If you have any questions - I'll be glad to help :)