Small update for you folks! The application process has been changed and you are now apparently able to update your application when before you simply received an error message stating you already submitted an application. This means you can update your application with new information if necessary.
Update: This applies to EU and NA. Also see the image below, it's the information you get after submitting your code.

There's also some teasing bits found in the fine print at
http://entry.ffxiv.com/na/index.html and related sections.
Here are a few of them:
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If you have received a FINAL FANTASY XIV promotional code for registering FINAL FANTASY XIII on the Square Enix Members site, please use it to apply for the beta test.
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If you have already applied for the FINAL FANTASY XIV beta test but would like to apply for the PlayStation 3 beta with a FINAL FANTASY XIV promotional code, please be aware that all previous applications will be invalidated.
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If an applicant applies multiple times, only the final application will be valid.
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The promotional code will also be required to obtain the FINAL FANTASY XIV secret in-game item, so please hold on to your code until the game’s official release.
So for those of you purchasing FFXIII, make sure to register the game at the Square Enix Members site! This will possibly help you, in the future or by updating your application, have a better chance at entering the FFXIV beta or the PS3 FFXIV beta.
And of course there's also the lovely "secret" in-game item that's promised, so don't lose the code!