It is indeed very intuitive to sort posts right within the admin posts interface. I have no complicated posts types or hierarchies to work with, so I have not found any problems with the more straight forward task of moving posts around within their respective categories. And the changes takes place in the front end almost immediately after changing the order in the back end (you may, of course, need to empty your cache to see the results).
I do have problems with posts that are assigned to more than one category. Moving them in one category, changes the order in the other category. I finally cloned the posts and gave them unique names for each category and it works just fine.
Also, if you start to move posts around within categories (or create clones of posts as I did) the order on your blog posts page will change as well (as would be expected). I found that the most recent post displayed on the blog page will be first (or top) post from the last category I moved posts in (so if I move a post around anywhere in category 3, the first (or top) post in category 3 will become the first post on the blog page.
Fortunately for me, I do not display a blog posts page on the site I am using this plugin on.
But for what this plugin does, it does it very well.
Thank you, hijiri, for developing this plugin for the WordPress community.