Space in WordPress Attribute Causing Problems

The way your code is written, you are breaking your div tag over several lines– literally like this, if you look at the generated source:

<div class="Container-Caption" 
        alt="Oh I have been to Ludlow Fair" 
        rel="http://www.link.com">
          blah</div>

I do not see any different between using a caption with or without spaces, but breaking your tag like that is non-standard, if not actually wrong ( and it doesn’t seem to actually be wrong based on some very quick research). It does look like the kind of thing that Javascript could choke on though. I’d suggest rewriting that so that it generates a bit more typical markup.

function Shortcode_Caption( $atts, $content=null ){

   // DEFAULT ARGUMENTS ARRAY       
   $args=shortcode_atts( array(
    'caption' => 'Caption',
    'link' => 'http://www.link.com'
   ), $atts);

   // ENCLOSED SHORTCODES
   if($content){
      $ret="<div class="Container-Caption""; 
      $ret .= ' alt="'. $args['caption'] .'"';
      $ret .= ' rel="'. $args['link'] .'">';
      $ret .=  $content.'</div>';
      return $ret;
   };
};  

add_shortcode( 'mycaption', 'Shortcode_Caption' );

echo do_shortcode('[mycaption caption="Oh I have been to Ludlow Fair" ]blah[/mycaption]');

Also note that you are breaking a rule specifically spelled out in the Codex:

Shortcode names should be all lowercase and use all letters, but
numbers and underscores should work fine too. Be wary of using hyphens
(dashes), you’ll be better off not using them.

http://codex.wordpress.org/Shortcode_API