Changing read permissions on /private/etc recursively
Changing the permissions on /private/etc/sudoers is definitely a no-no. The sudo command will fail to work if that file's permissions are not 0440 as you are noticing. This is a security measure -- the command distrusts any permission setting that is less restrictive than 0440 as it allows for potential tampering with sudo permissions on the box.

Normally you'd boot in to single user mode to fix this problem. This lets you log in with elevated privledges so you can do a:

chmod 440 /private/etc/sudoers


and get your sudo command back.

But I found this article that had an alternative that doesn't require a reboot and works if your account has Administrator level access. I haven't tried it, but it seems sound.

Open a Finder window a hit Shift-Command-G to get the "Go To" dialog. Enter /private/etc in the dialog and hit the Go button.

Find the sudoers file in the Finder window, select it and press Command-I to open the information window for the file and change the permissions on the file so they match:



Close the information window and you should be back in business.

All this being said: I would strongly encourage you to rethink changing the permissions of everything under /private/etc to be world readable. This poses a serious security risk (as seen from the way sudo locks you out when you make /private/etc/sudoers world readable) to your machine. Maybe there's another Ask Different question here that'll help you solve a problem you think you're solving by making these unsafe changes?