How do I copy files off a failed system partition without encountering permissions problems?
The simple solution to this is to reset all the permissions on all copied files to everyone read/write and let the system handle fixing them.

Reset all the permissions on a folder and its contents recursively with:

chmod -R 777 /path/to/folder


Then, run Repair Permissions in Disk Utility, and reset the ACLs on your home folder using the ACL tool on the Recovery HD:


Boot into the Recovery HD using ⌘R.
Run resetpassword in Terminal (available from Utilities → Terminal).
Select your account from the drop-down list.
Click the Reset button for Reset Home Directory Permissions and ACLs.