I noticed the problem when I went to view the admin logs on one of galleries, and it came back page not found. As it turned out, the debug.log file was over 900mb in size and I noticed in the PHP error log:

[28-Jul-2014 18:36:27 America/Chicago] PHP Fatal error: Call to undefined function zp_loggedin() in (path)/zp-core/reconfigure.php on line 110

I looked at the debug log (ftp'd it to pc) and it was full of this:

{17755:Mon, 28 Jul 2014 23:36:38 GMT} NOTICE: Use of undefined constant ADMIN_RIGHTS - assumed 'ADMIN_RIGHTS' in (path)/zp-core/functions.php on line 2051 zp_loggedin called from checkSignature (reconfigure.php [110]) from reconfigureAction (reconfigure.php [12]) from require_once (functions-basic.php [173]) from require_once (functions.php [17]) from include (index.php [14]) from index.php [32]
I then looked at my raw apache logs and found a whole heap of requests from 192.114.71.13 including one where it tried to run the setup script (I had protected them via the admin interface).

Found a lot of info about this IP here: http://www.projecthoneypot.org/ip_192.114.71.13

Anyway, I'd suggest everyone ban this one. I re-created an empty debug.log file and the logs page is now working again. Ugh..

Thanks for the info.