This is probably due to your thumbnail size settings.
Here is a story to explain:
I have a gallery of two images (A & B). They currently have thumbnails of 200x200px. I decide image A should probably have a different size.
I regenerate the thumbnail for image A. A dialog pops up. I enter in 150x200px.
Now, my standard setting is 150x200px. You can even go look in NextGen gallery options to see.
This means, when I edit a thumbnail, even if the thumbnail is currently 200x200px, it will recreate it as a 150x200px thumbnail. This is quite noticeable in this instance, because the "box" I can create is not going to be square.
Basically, when you regenerate a thumbnail, it alters NextGen's default thumbnail size, affecting the edit thumbnail process.
-----As for the whitespace, here is what I would do------
I've looked at the site and did some calculations. Based on the settings (width of page, margin, etc), the perfect width for your thumbnails is 192px for 3 images in each row. You would probably want to include a multiple of 3 images on each page (so go to settings and set 9 or 12 or whatever images per page).
The full image size you are working with is 450x600px. The way I see it, you have two options:
Make the thumbnails 192x256px. This will allow the thumbnail to include the entire image.
Make the thumbnails 192x192px. This will require you to edit each individual thumbnail if the face isn't present.
All of this assumes everything else stays the same, including the width of the content area, the margins, padding, etc. It also assumes you want 3 images per row. Let me know if you had something else in mind.
I also noticed that when you click an image, you are brought to a slideshow page. The image is stretched larger than its size. When you click the image, it brings up a lightbox, and the image is actually smaller. You might want to make the image smaller on the slideshow page and drop the lightbox completely.