Well, unfortunately i'm not very good in programming
So what i did: i tried to update existing plugin to latest FB scripts. In fact i've got strange effect: in standard theme i have fb like / fb comment forms, but in mobile they were disappeared 
Ok. Ignore the link I posted How to add facebook comments with function dispaly_image not display_media:
http://forum.coppermine-gallery.net/index.php/topic,76925.0.html in Reply #25.
I am going to tell you step by step how to add facebook comments (
https://developers.facebook.com/docs/plugins/comments):
1) Add to mobile_light/theme.php before ?> (Replace in the code data-width="300" with the value you want 250,500 etc. Facebook comments are not responsive thats why I choosed 300) :
/******************************************************************************
** Section <<<theme_display_image>>> - START
******************************************************************************/
function theme_display_image($nav_menu, $picture, $votes, $pic_info, $comments, $film_strip)
{
global $CONFIG, $LINEBREAK;
$superCage = Inspekt::makeSuperCage();
$width = $CONFIG['picture_table_width'];
echo '<a name="top_display_media"></a>'; // set the navbar-anchor
starttable();
echo $nav_menu;
endtable();
starttable();
echo $picture;
endtable();
if ($CONFIG['display_film_strip'] == 1) {
echo $film_strip;
}
echo $votes;
echo '<div class="fb-comments" data-href="http://www.lightphotos.net/photos/displayimage.php?pid='.$pid.'" data-width="300" data-numposts="3" data-colorscheme="light">';
echo '</div>';
$picinfo = $superCage->cookie->keyExists('picinfo') ? $superCage->cookie->getAlpha('picinfo') : ($CONFIG['display_pic_info'] ? 'block' : 'none');
echo $LINEBREAK . '<div id="picinfo" style="display: '.$picinfo.';">' . $LINEBREAK;
starttable();
echo $pic_info;
endtable();
echo '</div>' . $LINEBREAK;
echo '<a name="comments_top"></a>';
echo '<div id="comments">' . $LINEBREAK;
echo $comments;
echo '</div>' . $LINEBREAK;
}
/******************************************************************************
** Section <<<theme_display_image>>> - END
******************************************************************************/
2) Add to mobile_light/template.html after <body> (without this code the facebook commets don't show):
<div id="fb-root"></div>
<script>(function(d, s, id) {
var js, fjs = d.getElementsByTagName(s)[0];
if (d.getElementById(id)) return;
js = d.createElement(s); js.id = id;
js.src = "//connect.facebook.net/en_US/sdk.js#xfbml=1&version=v2.3";
fjs.parentNode.insertBefore(js, fjs);
}(document, 'script', 'facebook-jssdk'));</script>
Another way I belive you first used Social Sharing Plugin (Facebook Like/FB Share/FB Comments/Twitter/VZ zeigen)
http://forum.coppermine-gallery.net/index.php/topic,70221.0.html If you still want to use it then ignore the code above, go to plugin manager - Social Sharing (social_sharing): v1.5 - Configure plugin - under the title/caption (see attachment Configure plugin.jpg). Under the picture option adds the facebook button and comments inside the display image td. That's why the picture navigation plugin arrows go down, not on the center of the td (see attachment under the picture.jpg). Under the title/caption adds the facebook button and comments outside the display image td (see attachment under the titlecaption.jpg).
another problem is that then picture navigation plugin is installed - i have a problem, but then it is deinstalled - seems all is okay. How you manage to get this plugin work well?
Is proabibly the Share plugin you use. Is inside the display media td. Should be outside. Can you post the link from where you downloaded this plugin? Does it has the option to place it under title/caption like the facebook plugin?