Validate user meta and redirect

Here is how I would do it:

function save_extra_user_profile_fields( $user_id ) {

  if (!isset($_POST['address']) || empty($_POST['address'])) {
      // this field was not set or was empty
      // do your action
      wp_redirect( home_url() );  // or profile page
      exit;
  } else {
      // field was set and contains a value
      // do your action
      update_user_meta( $user_id, 'address', $_POST['address'] ); 
      wp_redirect( home_url() );  // or whatever success page
      exit;
  }
}