Well, I fixed the problem, i think.
I've added one line of code to the plugin, at the bottom of the elseif statements:
Code:
} else {
$sql = "UPDATE " . TABLE_PREFIX . "session SET browser='unknown' WHERE userid='".$db->escape_string($vbulletin->userinfo['userid'])."'";
}
Now the people who use a browser that is not detected by vBulletin don't get a sql-error no more.