"/etc/sudoers is world writable" on Mac OS X Mavericks

Finder -> Go -> Go to folder

and enter /etc/sudoers and push Go button. Right click on the sudoers -> click on get info -> change permission to: System: Read & Write Wheel: Read Only Everyone: Read Only

Lock it and open a terminal and try again.

All the best!

Finder → Go → Go to folder:

and enter /etc/sudoers and push Go button.

Right click on the sudoers and change ther permission.

1.Enable root user:
System Preferences -> Users&Groups -> Login options -> Network Account Server -> Join -> Open Directory Utility -> Edit(menu) -> Enable Root User

2.switch to root,change /etc/sudoers permissions
$su
$chmod 440 /etc/sudoers

Open Disk Utility, select you disk and click "Repair Disk Permissions"