TinyMCE input format is set to "Full HTML" but code is still being stripped
Assuming that the stripped tags in question are mostly things like embedded CSS style tags you might need to enable the Full Page plugin to allow them in your content, apparently having style tags in regions apart from HEAD tag is not the best practice and that's the reason the functionality is not enabled out of the box from my understanding. Also assuming that you have the WYSIWYG module with TinyMCE library installed for your cause and not the TinyMCE module, here's a sample code of how I enabled the full page plugin in my case. (The code goes in your custom module, replacing your module name with MYMODULE in the function name).

/**
 * Implementation of hook_wysiwyg_plugin
 *
 */
function MYMODULE_wysiwyg_plugin($editor) {
  // if the editor is tinymce include the fullpage plugin so that embedded css is included
  $plugin_path = wysiwyg_get_path('tinymce');
  switch ($editor) {
    case 'tinymce':
      $plugins = array(
        'fullpage' =&gt; array(
          'path' =&gt; $plugin_path . '/jscripts/tiny_mce/plugins/fullpage',
          'buttons' =&gt; array('fullpage' =&gt; t('Full Page')),
          'url' =&gt; 'http://www.tinymce.com/wiki.php/Plugin:fullpage',
          'internal' =&gt; TRUE,
          'load' =&gt; TRUE
        )
      );
      return $plugins;
    default:
      break;
  }
}