The default behaviour of Outlook with regards to sent items continues to come up on forums as an issue.
By default, when you send an email using the From field via your Send As permissions, the item you have sent goes in to your own Sent Items folder. This is because you sent it, not the person whose mailbox it was sent from. This can be useful from a tracking point of view (who sent the email).
However it may also be useful for the item to be stored in the Sent Items folder of the Shared Mailbox so that other users or even the mailbox owner can see what was sent.
How you achieve this depends on the version of Outlook that you are running. The version of Exchange doesn't matter.
For Outlook 2003 and 2007, a registry change is required, following the installation of an update. If you are keeping the machines up to date, then further updates should not be required.
These registry changes are outlined in the following articles:
Requires Outlook 2007 Hotfix: 970944
Requires Outlook 2003 Hotfix: 953803
For older versions of Outlook, you will need to look at third party tools. The only one that I am aware of are the tools from Ivasoft: http://www.ivasoft.biz/
For OWA, you will need to use a server side tool, again the third party tools from the above site are the only ones that I am aware of - and support for latest version of Exchange isn't available.
For Outlook 2010, no registry change is required, you just need to add the mailbox in a different way.
Instead of adding the mailbox as an additional mailbox through the Properties of the primary mailbox, add the additional mailbox as an additional Account. That means going through the new Account wizard again. This feature also allows you to have connections to another mailbox in another Exchange forest at the same time - I have used this to migrate public folders (see http://blog.sembee.co.uk/post/Cross-Forest-Public-Folder-Migration.aspx)
However if you are using Outlook 2010, you should also be aware of the issues in this KB article: http://support.microsoft.com/kb/2297543 (Performance problems when you try to access folders in a secondary mailbox in Outlook 2010).
(Late posting because I forgot to press publish).