Well, in my Mpmanager line 51(include/search.inc.php) is

$sql = "SELECT msg_id, subject, from_userid, to_userid, msg_time, msg_text FROM ".$xoopsDB->prefix("priv_msgs")." WHERE (to_userid = ".$xoopsUser->getVar('uid').") ";

$xoopsUser is not a object if you are a anonym user so:

this lines are not very useful:

$gperm_handler =& xoops_gethandler('groupperm');
if (is_object($xoopsUser)) {
$groups = $xoopsUser->getGroups();
} else {
$groups = XOOPS_GROUP_ANONYMOUS;
}

You can change this to:
if (!is_object($xoopsUser)) { return false;}