Mail clients are prone to an astonishing variety of problems—more than I have room to write about in a year's worth of columns. However, the following problems and solutions are good examples of the kinds of client-related scenarios you're likely to face.
Outlook crashes when a user tries to open a particular message. This problem usually indicates that the message is corrupted. Sometimes you can fix the problem by removing the message or moving the mailbox to a different server. If the message in question is in a personal store (PST), you can try running Scanpst, which might solve the problem. In some cases (e.g., when a specific corrupted message causes Outlook to fail), you might need to use the Mdbvu32 tool from the Microsoft BackOffice Resource Kit (BORK). Mdbvu32 lets you isolate and remove the offending message directly from the server-side mailbox.
Messages disappear after the user reads them. Every instance of this problem I've ever encountered occurred because the user set a view to show only unread messages, then forgot that view was in place. Exchange Server just flat doesn't throw away email (although you might want to check the Deleted Items folder to see whether the user has been throwing messages away without realizing it).
Client launch times are unusually slow. Slow client launch times are usually related to an incorrect remote procedure call (RPC) binding order or to name-resolution problems. The Microsoft Knowledge Base is full of articles about how to resolve these problems.