New Facebook users see OTHER users data prefilled on registration page

Shawn,
Sorry for the delayed response.

The profile information thing is a new one to us.. and obviously a very bad problem if it's happening like you say. Privacy and security are things that Facebook (and we) take seriously. Not sure what would be causing that at all, but I have a few thoughts:
1) What is your caching setup like on your site? Mainly, do you have the System - Cache plugin or any other aggressive caching plugin enabled? The System - Cache plugin will cache the entire page before a user views it. I can only imagine that the page is being cached with the user's data filled in, and then the 'next' user is getting that data. With that said, we do a lot of testing and planning with that type of caching in mind, so it shouldn't be the case, but throwing it out there.
2) Do you know if the user's are testing from the same computer? Mainly, logging in with one FB account, logging out, and logging in with a new FB account? Again, should work, but need to narrow it down.

Finally, for the Invite Friends link.. what link are you talking about? What module from JFBConnect are you using to show that link.. the JFBCRequest module (or {JFBCRequest} tag)? Can you post a link to the page with that link so we can test? The link will also help check for some other odd configuration issues that may be causing the registration stuff above too.

Thanks,
Alex