It's about time this thing got under way. If you're participating in the private beta, you should receive an email to that effect.
If you were also a member of the V1.0 private beta, you'll notice we're doing things a little differently this time. There isn't a separate site for discussion, and we're not locking down access to the documentation.
All questions and bug reports (with one caveat, detailed below) should go on Stack Apps with the api-v2-beta tag. We'll be closing (and subsequently deleting) these posts as they're dealt with. You should not expect any posts created with the api-v2-beta tag to survive the beta.
The one caveat to bug reports: if you find what you believe is a privacy violating bug (these presumably have to deal with access_tokens), please report it to email@example.com.
Broadly speaking, the API should be functionally correct. Methods should return the data you expect in the manner you expect it (compression, encodings, etc., should all be correct). Naturally, the point of a beta is to find those cases where this is not true; if you come across any, please post them with the bug tag.
Towards the end of the API private beta, it will probably be necessary (depending on the changes that occurred during the beta) to regenerate filters. Instructions on how to do this (as well as whether it's necessary) will be sent out when the time comes. It would be in your best interest to make it easy to swap out filters accordingly (this is generally true, independent of the beta environment).