I got rid of the annoying gaps.
If you are using blender 2.6x, I found that unwrapping a flat plane like this, you can scale the image width. It seems that it ignores your efforts to trim the top and bottom ends of your image (for some reason). I had to go back and edit the image in gimp: I scaled the image up and reduced the canvas size to 256x256. This cleaned up the image. Gimp also has a cool little perspective tool that I used to fix the aspect of the original picture. The bottom of the image was a wee bit skinnier that the top, which is fixable.
Thanks for the input Hack, Chacal and jpeters!