It would be ideal to see a list of emails that have "hard bounced" once, thrice, however many and be able to select the lot of them and delete/archive them. This is a challenging thing to do at present. If there is something I am missing please let me know.
Emails that are undeliverable (hard bounces) will automatically be moved to error so that they are not tried again without some further action. Error exists to help catch these emails so you can revisit them and see what could have caused a bounce (format reasons, specific domain trends, etc.). You are also able to see email history for a contact by going into that particular contact record and selecting 'emails'.
Contacts in error will have no impact on your billing for future billing cycles past when you initially added them (they do not count as active contacts).
Does this information help? Certainly let us know if there is functionality you are looking for that may not exist, is there a particular reason you are wanting to archive bounced emails?