You might want to consult the original recipe by Jim Lahey in "My Bread" to which Bittman gives full attribution.

Try another brand of flour and consider adding some gluten.
Also, weigh the flour using a digital scale.
Here's bit that's more in-depth on the why's and how's of the no-kneed recipe. With quantities in weights.
http://blog.khymos.org/2010/12/22/no-knead-bread/#more-526

I did the Bittman No Knead method for a while, then I got tired of making a new batch of dough every time I wanted to bake some bread. I found the method from "Artisan Bread in 5 Minutes a Day" is a good way to take the no knead recipe and extend it for a week or two without having to make a new batch each time. And, like the others have said, over time the dough takes on a good sour flavor over the course of a week or so.

oops, that wasn't mine (I just found a good example on Flicker.) The old dough develops tang over time and I just store it in the fridge if I'm not making another loaf the next day. Good luck with your no knead adventure.

How long did you let it rise? Bittman preferred it with an 18-hour first rise and a 2-hour second rise. If you want a shorter rise (12-hour) he suggests you add an extra 1/8th tsp of yeast. I suggest you read the article that accompanies the recipe in case it gives you any clues to help improve your loaf. http://www.nytimes.com/2006/11/08/dining/08mini.html?pagewanted=1&_r=1

The old dough addition sounds like a good idea. My loaf does look very similar to yours! Thanks for the response...

I usually get a loaf that is perfect, well full of elastic air pockets and a crisp crust. Maybe you are used to lighter weight breads, but my first guess is that you need to try again. Does yours look like this? I also use an 'old dough' method when I save some dough from previous loaves to use in the next one.
http://www.flickr.com/photos/hlk/389341090/