Is it possible to assign a group of users the ability to view the inbox and the subjects of a mailbox, but not be able to open the items?

no, the minimum permission is review which can read all items within the folder

Not in the inbox. The calendar is a different animal. What is the goal? Why the need to do this?

Question is same, what's your goal and which version of Exchange do you use? If you want to let the user to read just subject lines then you can enable message tracking with subject logging and ask end user to track all the messages sent/receive by user... But this will enable subject reading for all the users available on a server and thegranularitylevel of permission is not possible. Also this can give the result for 7 days (or the duration you configured in message tracking). Positive thing is, message tracking can search all the mails which are sent/received by the user even though it is deleted from mailbox. You can configure message tracking for non-admin users with below procedure... ENABLING MESSAGE TRACKING FOR NON-ADMINISTRATOR ACCOUNTS http://blogs.technet.com/benw/archive/2006/12/08/enabling-message-tracking-for-non-administrator-accounts.aspxAmit Tank | MVP Exchange Server | MCITP: EMA | MCSA: M | http://ExchangeShare.WordPress.com

Exchange 2007.We are using Microsoft Dynamics CRM, our emails are tracked in the system by having them all forwarded to a mailbox which is monitered by the CRM software. Unfortuantly some emails cause the email routing system to fail, and they need to be manualy removed from the CRM mailbox. I do not want the people in charge of flushing the email system to be able to view the contents of the emails.Thanks