Using AJAX callbacks in user edit form invalidates one-time password reset

To reproduce:

1. Ensure an address field is attached to users, and editable by themselves when editing their profile.
2. Use the one-time login link mailed to you when creating a new account or using the "Request new Password form"
3. Clicking the "Login" button, you will be redirected to your user profile.
4. Fill out a new password or change the email address. There will be no "Current password" field to fill out, as expected.
5. Change the country from the drop-down in the address block.
6. When submitting the form, the following error appears: "Your current password is missing or incorrect; it's required to change the Password."

Workaround: Naturally, do not change the country field when changing the password or email.

At http://drupal.stackexchange.com/questions/20947/user-cannot-change-passw... a user reports a similar problem and speculates it's due to the AJAX request, which may be invalidating the token that dismisses the current password requirement, or may be rebuilding the form and changing the token.