For this Pang 96! pic, I didn't even try to use Photoshop's clone stamp tool, which takes a cursor-sized piece of material and copies it where you want, because said tool works best when you have either an irregular background, like the water in the Sailboat pic. With a pattern like the tiles here, I decided to take two screenshots, each with the sprites on each side. Then I copied the clean half of one, and put it over the same half with the sprites on the other. I wish I had thought of this technique ages ago, as it turns out to be much easier than either clone stamping or copying smaller squares. With the grid view (accessed with the "ctrl" and ' keys,) and with Adobe Photoshop CS4's alignmnet indicator (that shows with a pink line when the edges of each of your pieces are lined up, I was able to essentially line up the copied half of the picture with the other half.
By the way, when digging up that sailboat post I linked to, I noticed that one post was missing its picture. Don't know how that happened, but I have rectified the situation.