There seems to be a problem when trying to move a wishlist item into a category. I tried a few times with a few items. I tried with only about 5 items thinking maybe the page was timing out and still when I select the categories and click "update wishlist items" Nothing saves. They are all still right where they were (which in my case is in the "no category" list).
Try sorting from the top of the list down, your list is probably too long for you to sort it otherwise.