@spriteyone, yes the permalink edit and the slug do exactly the same thing. Generally changing a slug should not be an issue unless what you change it to conflicts with another permalink. Example.
This is the permalink for a yearly archive:
Let's say you have a page where you made predictions about 2011 titled "my predictions for 2011." The standard permalink would be blogname.wordpress.com/my-predictions-for-2011/ . Now let's say you decided to shorten the slug to just 2011.
This would be the permalink for your page with the changed slug: blogname.wordpress.com/2011/
Note that the page permalink and the 2011 archive permalink are both the same?
This is where people run into problems because the wordpress software then does not know what to give you and by default just serves up the 2011 archive. This is something that wordpress needs to work on and figure out a way to keep it from being an issue. (I should note though that I have not tried this lately, so perhaps they have put something in place to stop it.)