The first looks for the manager directory and the content of the login page, starting with:
<title>MODx CMF Manager Login</title>
It also includes the instructions to login, so if you’re not running a site in English or if you change the title tag, this technique won’t work.
I believe the second was fixed with 1.0.3 release via the AjaxSearch version included there.
Chain both together and tweak the second one and you could have problems indeed if you’re running an un-patched version of MODx.