How do I add a simple form to the node edit page?
It sounds like you want to let the author notify your module of significant changes to a node.  Another approach you could take is to add a field to your node type, such as "field_change_notification" (boolean/checkbox) ... then look to check if the author selected the checkbox in hook_node_presave.  You can even set it back to unchecked so they can again notify your module on the next update.

function HOOK_node_presave($node){
  if ($node-&gt;type == 'article'){
    if ($node-&gt;field_change_notification['und'][0]['value']){
      drupal_set_message('A change has been made...');
      $node-&gt;field_change_notification['und'][0]['value'] = 0;
    }  
  }
}