For updating Core - as stipulated in the previous post - even IF you have a great backup system... you may be stuck waiting 4 hours for your admin to get around to restoring your demolished directories. My next attempt, I renamed my heavy 'sites' directory to 'zzz' or something of that order and then proceeded to delete the contents of the core directory I had access to. Then using CyberDuck I copied over the contents of my D7.2 directory and returned my sites directory to its previous state.
I realised that when updating Drupal 7 (copying all files to your working directory using the likes of CyberDuck) - you need to make sure that you copy the .htaccess file which is hidden on most computers by default (there's also a .gitignore file in D7.2).
To view the hidden files on a Mac -- open a terminal and type in "defaults write com.apple.finder AppleShowAllFiles -bool true". You will then need to log in and then log out to reset Finder. (Ref: http://guides.macrumors.com/Viewing_hidden_files_on_a_Mac, to turn off again replace 'true' with 'false').
In the event of a white screen...(of Death!)
Type the following on the third line of your index.php file.
Echo "Blah";
If you see the word "Blah" appear on your site - you know that PHP is working and you've got an internal Drupal problem (not the server, or permissions, etc etc).
What next? Slow and steady... I plodded along.
Check if your administration pages are working. I had the interesting case where my frontpage was not working but everything else was! Knowing that my modules were not up to date - my first job was to update them and then to disable them one by one until I found the culprit that was breaking my frontpage. (Re-cap: I was working on a site that I created over six months ago and using a pre-release version of Drupal 7 and associated pre-release modules - Views, Link, Ctools, Biblio, acl, forum_access, field_group, wysiwyg).
When I went to update my modules - I noticed that Forum_Access now depends on both acl and chain_menu_access. Because of this new dependency, simply droping the new versions in without downloading and enabling chain_menu_access first would surely mess up things on my site. I suspect that gem, Drush pm-update, does all of this without me being aware - but given that I have to find the cumbersome manual way of doing things... it was quite the revelation.
I also uninstalled any modules I knew that I was not using, in this case Panels. Becareful about uninstalling modules since this also deletes any data created by the module. That is the warning it gives you and when you think about modules like Views - you really don't want to delete some things by accident.
So all of the old modules deleted, all of the new modules downloaded to my computer and copied over via CyberDuck. I ran the update script. Victory! My frontpage is working again! *Insert little dance of Joy!* I enabled the modules that I had disabled and was prompted to rebuild permissions (for chain_menu_access). That done, my frontpage was still working. Satisfied, I took a break.
... it only took three days (the few hours I had to work on it per day).