Cannot Select Recipients in CiviMail in 4.6.2
Thanks. It's helpful to report these kinds of issues along with details of the configuration (like you did) and any steps required to reproduce in a new installation.

For a temporary work-around, you might try using the old, deprecated UI by editing civicrm.settings.php to include define('CIVICRM_CIVIMAIL_UI_LEGACY',1);

FWIW, we still have a couple issues that are getting reported by multiple people but which we cannot reproduce yet. Based on the data-points so far, the use of Joomla with Civi 4.6.2 seems to be a common theme, but that could be coincidence. More reports/debugging is greatly appreciated.