If you believe it is NextGEN's thumbnail creation function causing the problem then consider reporting it as a bug here http://www.nextgen-gallery.com/report-bug/. I have seen numerous nextgen users with that sort of issue.
I used the firefox browser plugn firebug to test changing the height of http://www.codyphotography.com.au/wp-content/gallery/families/dsc5205.jpg (3rd row, last thumbnail on right) to 240px to match the other thumbnails and it corrected the layout issue at that point in the display. It's odd you say recreating the 239px high thumbails at 240px high does not fix the problem. Keep in mind you do have several 239px high thumbnails and you ideally need to resize them all.
You can try circumventing the problem by adding this css .ngg-gallery-thumbnail-box {height: 240px } which will remove the gaps in the display but obviously it can't remove the small black lines under the short photos.