Turns out there’s a pretty easy fix for this using the Finder, so long as your account has administrator privileges:

Steps:

1. In the Finder, go to /etc (or do <cmd>-<shift>-g and enter /etc, if you don’t see it in the Finder)
2. Get Info on sudoers
3. In the Info window’s Sharing & Permissions section, add an entry for your local user with read and write access
4. With a text editor, edit /etc/sudoers and fix the problem.
5. Fix the permissions on /etc/sudoers back to 0440.
6. Enjoy your newly-regained sudo power!

Of course, this can be used to overcome other permissions problems too.

If only visudo had a validator, along with a syntax checker…