Upgrading from Joomla 1.5RC4 to Stable (Production) was a breeze. There was no need to make changes to database structure or anything. Simply download the full stable release, upload to my server, and overwrite the files. Here's how I did it from the shell.

Navigate to the proper directory:
$ cd /mysite/

Download (wget) the new compressed file:
$ wget http://joomlacode.org/gf/download/frsrelease/5078/21064/Joomla-1.5.0.tar.gz

Uncompress over old files:
$ tar -zxvf Joomla-1.5.0.tar.gz

Remove the installation directory:
$ rm -fR installation

I then visited the site to check to make sure everything was working. Sure enough, it all worked great! I would highly recommed creating a backup of your site files and database. Here are some links from my site on how to do this from the shell:

Create a MySQL Backup from Shell
Create file/website backup from Shell