Catch-All Exchange Mailbox

Environment: ~50 users on local Exchange 2010 running on Server 2008 R2.

Management wants a mailbox that will absorb all incoming and outgoing emails from customer service employees. Any ideas on how best to accomplish this? Obviously incoming is no problem (just forward mail to the catch-all mailbox), but I'd like to automate outgoing (all I can think of right now is to have users BCC the catch-all).
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Please clarify what you are asking for.

a catch-all will catch all email no matter their source.

i think what you are looking for is an exchange rule that deals with when a message is addressed to a group of emails or is being sent by the same group to have a copy of that email forwarded to a central/single mailbox.
Shared mailbox, (record keeping customer service interactions)...

Not sure this option is available on the version you are on.
Server based rules on the incoming transport for delivery to end user determination/forwarding.
Server based rule on the SMTP transport for outgoing email..

Note that it only will capture events on the outgoing side so long as your users used your mail server to send/respond to the notices.

Under 2013 you are looking at mailflow.

An EE Article by Glenn Night, while having a different purpose, could be used as a reference and an example for doing what you've been asked.

note in the step by step you will have two rules. one in step 1 you will choose the recipients (to, CC) are the email addresses of interest, for the second rule you will choose the senders as those same email addresses.
It might be simpler to use security in both rules such that you do not have to keep adding/removing users from these rules, but rather add remove the users for the security/distribution group when they fall out of the group of interest.

test the rule, you could add labels as detail to make it easier to distinguish the incoming email from the outgoing emails.
The action will be to blind carbon copy to a separate mailbox.

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