The new online ESTA system isn't a Visa! You will still get the green Visa Waiver form on the plane until 12th Jan next year when the ESTA takes over full time. If you needed to get a Visa then the reply to your ESTA form application would have said so. ("You may NOT travel without a valid Visa, please contact your local Embassy for Visa advice").
Look here for more about moral turpitude;
http://en.wikipedia.org/wiki/Moral_turpitude
You will see that even drunk driving isn't classed as "moral turpitude"
Enjoy your trip and stop panicking!