To check for a hidden file in the home directory, in the Nautilus file manager select [View][Show Hidden Files]. That'll show files starting with a fullstop, eg .xyz, and in the home directory there will be lots of them. Those hidden files are roughly cookie files and folders holding the user settings.
Editing the PostSession file makes some sense but I don't know why it's not being setup appropriately that it closes down in a good way when user shuts the computer down.
This is a guess that might prevent you needing that: In Truecrypt [Settings][Preferences][Background Task] maybe background task is ticked [Enabled] and then running but not obvious as an icon in the notification area and so as you try running another instance of Truecrypt, it doesn't like it?
Maybe untick [Enabled] if it is ticked and see if that helps. Mine is unticked and I haven't a problem with it shutting down. That said I don't know how it unmounts at shutdown, it just works and I don't see errors. I guess each new session it might delete the stale lock file, if it's not closing in an ideal way.
I don't know where you're seeing the message that it's obvious enough to be a problem for other users. Always better to have it tidy though. I'm assuming you're using the graphical interface and not doing it the hard way though terminal.
To edit a system file the like of those in /etc you need to be logged in as superuser/administrator or use sudo command. Each time you do that a hidden backup is created as ~oldfilename in the same location.
'edit' as a command isn't an editor, it's mailcap to determine the filetype and the program that might open it. There are a lot of text terminal editors but not as easy as the graphic ones.
So, if it isn't the background task running where it's not needed then maybe do try the PostSession shutdown command with editing as
Also you can do
sudo gedit /etc/gdm/PostSession/Default
navigate to the file you want, right click and open with gedit or another editor. However, be very careful navigating as superuser! You might do something you regret with all that power to hand.
Final point so you're aware, if you do want to login as superuser, then use "su -" to login as another user use "su username".