It you did a clean install from 12A269, you don't need to do a thing. As an Apple Seed participant here is an email I received yesterday announcing the closing of the beta:
Thank you!
The final version of OS X Mountain Lion 10.8 was released today! Your 12A269 redemption code actually purchased the final version for you! The last build we seeded, 12A269, is identical to the build that is being sold in the Mac App Store today. There is no need for you to purchase another copy in the Mac App Store.
We would like to take this opportunity to sincerely thank you for participating in the seed process. Many bugs and issues have been discovered as a result of your efforts. You have contributed to the overall quality of our product.
We realize that testing involved a great deal of time on your part to submit bugs, submit follow-up information, and re-install software along with your daily work. We appreciate your dedication.
At this time, we do not need any new bug submissions. We will keep the project open for now, so that any already-writtten bugs can be fully diagnosed.
You will continue to have access to your participant page at
https://appleseed.apple.com, and we encourage you to keep your information up to date. We will be sure to consider you for future seed projects.
Apple Software Customer Seeding