Can't access /etc folder in OS X Mountain Lion
Hit ⌘+⇧+G (or select Go - Go to Folder... from the Finder menu bar) and enter /etc or any existing and readable path as the target location to browse it.

Given you enabled showing of hidden files, while double-clicking etc from Finder does not work, you can still right-click it and choose Open from the context menu.

The system-wide configuration files in /etc are best to be treated with caution just as all the other hidden system files and therefor I'd certainly not recommend changing permissions for them, but if you do need to view or edit them I would suggest doing it from the Terminal. This will also make it easier to gain the necessary root privileges for changing them by using the sudo command.