img with relative src-url not working

No, it is not fixed. Some pictures have absolute src-urls on other servers and they work fine.
I am actually not sure how the user edited the story but since it's not a user with root access not direct server access, it must have been through the general image-upload function. at any rate, if you want this module to properly display drupal pages in facebook it should provide for such cases. The following hack accomplishes the task, but you properly want it more properly integrated.:

function absolute_url($txt){
  $base_url = 'http://'.$_SERVER['HTTP_HOST'];
  $needle = 'src="';
  $new_txt = '';
  $new_base_url = $base_url;
  $base_url_parts = parse_url($base_url);
    while($pos = strpos($txt, $needle)){
      $pos += strlen($needle);
      if(substr($txt,$pos,7) != 'http://' && substr($txt,$pos,8) != 'https://' && substr($txt,$pos,6) != 'ftp://'){
        if(substr($txt,$pos,1) == '/') $new_base_url = $base_url_parts['scheme'].'://'.$base_url_parts['host'];
        $new_txt .= substr($txt,0,$pos).$new_base_url;
      } else {
        $new_txt .= substr($txt,0,$pos);
      }
      $txt = substr($txt,$pos);
    }
    $txt = $new_txt.$txt;
    $new_txt = '';
  return $txt;
}

and then in page.tpl.php change:

<?=$content?>

to

<?php echo(absolute_url($content)); ?>

Yeah, I don't think you get around changing all the relative src-urls. Else DFF will simply not be compatible with lots of modules.

Your img_assist is a perfect example thereof. If you use all the standardoptions, it inserts a html-snippet like the following:

<span class="inline left"><img src="/files/images/Photo 18.thumbnail.jpg" alt="et testbilde: dette er bare en test!" title="et testbilde: dette er bare en test!"  class="image image-thumbnail" width="100" height="75" /><span class="caption" style="width: 98px;"><strong>et testbilde: </strong>dette er bare en test!</span></span>

If you instead choose the "filter tag" it inserts:

[img_assist|nid=1398|title=et testbilde|desc=dette er bare en test!|link=none|align=left|width=100|height=75]

which translates into:

  <div class="content"><p><span class="inline left"><img src="/files/images/Photo 18.thumbnail.jpg" alt="et testbilde: dette er bare en test!" title="et testbilde: dette er bare en test!"  class="image image-thumbnail" width="100" height="75" /><span class="caption" style="width: 98px;"><strong>et testbilde: </strong>dette er bare en test!</span></span></p>
<p>nncnnc</p>
<div class="image-clear"></div></div>

Loads of people will use the html-mode. And I think you'll have to calculate that most if not all will use the DFF as an alternative presentation mode for their data, not as the only mode. That is why you either need to change all modules to produce different html-output that is DFF compliant AND works with the regular http-display, or you need to filter through the code like I did.

on 1: doing string replacement in text can hardly be very work intensive, compared with tasks such as serving images

on 2: You probably are right. I just don't know what th proper way of referring to the original domain name.

on 3: I don't get it. when would that happen? "href" statements aren't changed, so it only happens when "src" is invoked, and only if no domain name is given. Cna you give me a code example where this would cause problems?

ok, point taken. Makes sense to be able to turn it on or off. But not supporting img_assist without the user having to hack the main files really would make the module unusable for most cases, or not?