Consider sites/*/libraries or use of Libraries API

One big plus for this one. There's absolutely no reason to load the Simple HTML library on each page load, as it does now. When using the Library API you'll make it possible to load the Smple HTML library only when needed using drupal_add_library().

/**
 * Implements hook_libraries_info().
 * Add the PHP Simple HTML DOM Parser to Drupal's library register.
 */
function simplehtmldom_libraries_info() {
  $libraries['simplehtmldom'] = array(
    'name' => 'PHP Simple HTML DOM Parser',
    'vendor url' => 'http://simplehtmldom.sourceforge.net',
    'download url' => 'http://sourceforge.net/projects/simplehtmldom/files/',
    'version arguments' => array(
      'file' => 'simple_html_dom.php',
      'pattern' => '/Version\: ([0-9.]{1,})/',
      'lines' => 10,
    ),
    'files' => array(
      'php' => array('simple_html_dom.php'),
    ),
  );
  return $libraries;
}

Skilip's solution is much better, but for anyone else out there trying to implement this, make sure the simple html dom library is extracted into sites/all/libraries/simplehtmldom. The folder name needs to be the same as the key in $libraries. Also, the latest 1.5 version of simple html dom, is v1.5 and this is printed differently in the php file, so the regex needs to be changed. Here's what worked for me:

function simplehtmldom_libraries_info() {
  $libraries['simplehtmldom'] = array(
    'name' => 'PHP Simple HTML DOM Parser',
    'vendor url' => 'http://simplehtmldom.sourceforge.net',
    'download url' => 'http://sourceforge.net/projects/simplehtmldom/files/',
    'version arguments' => array(
      'file' => 'simple_html_dom.php',
      'pattern' => '/version ([0-9\.]+)/',
      'lines' => 40,
    ),
    'files' => array(
      'php' => array('simple_html_dom.php'),
    ),
  );
  
  return $libraries;
}

Provided patch includes several changes, such as:

• Removed simplehtmdom library
• Implemented hook_libraries_info (solution from #4)
• Added README.txt with installation instructions
• No dependency added, the module will work nicely w/o Library API as well as with it.

Please review.

P.S. Please use git apply --index to apply the patch.

If you don't have time please give me necessary permissions and I'll do everything myself.

Commited patch #5 04d9593 with minor text modifications.
New release 7.x-2.x created https://drupal.org/node/2187329