I see a lot of double quotes in your coding

And you have a lot of double ifs and elses with no coding in it.
The structure isn't bad, just some small things that can be fatal in a production environment.
PHP Code:
$rows = mysql_num_rows($userq);
if($rows >= 1)
{
$value = 1;
}
else
{
$value = 0;
}
return $value;
Or just use
PHP Code:
return (mysql_num_rows($userq) == 0);
____
Reading throught the source some more and I can see a lot of unfinished and exploitable code.
First off all use concentrated strings with single quotes, second don't use require_once but use require (remove all the includes on top of the classes -_-).
$user_data[''.$value.''] WTF? $user_data[$value] would be better.
$username = $_POST["username"];
$query = mysql_query("SELECT account_name FROM users WHERE account_name = '".$username."' LIMIT 1;");
Exploit.
if($GlobeUsers->GetBadges($_SESSION['account_name']) >= "11" && $GlobeUsers->GetBadges($_SESSION['account_name']) <= "13")
{
}
else
{
$GlobeSecurity->Redirect("maintenance.php");
}
can be changed to
if(!($GlobeUsers->GetBadges($_SESSION['account_name']) >= "11" && $GlobeUsers->GetBadges($_SESSION['account_name']) <= "13"))
{
$GlobeSecurity->Redirect("maintenance.php");
}