Nick -- Understand I am not a programmer, but I can hack around and read the great stuff you have written here.
Simply put it looks like since the call to the Control Panel is often without and "?" QUERY_STRING being referenced, the resulting behavior in PHP is to flag an error based on the default php.ini error_reporting= setting. http://bugs.php.net/bug.php?id=12325
Would be nice if you could put a sanity check (better you do this with clean programming vs some real nasty hack by me)... to make sure any use of QUERY_STRING is only used if it passes isset(). Clearly this is in v1.2.5 cpanel.template.php... but also looks like it might be good to do in the other locations.. best I can tell (and suspect you can find better than me, so humble list here from me):
lib\Pager.class.php [this one is already checking isset()]