This page should have a lot more information about Exchange. For now it's just a collection of notes.
My understanding is that Office 365 (and Exchange Online) is largely just a version of Exchange hosted by Microsoft. Many of the issues listed here that apply to newer versions of Exchange may also apply to Office 365 and vice versa.
Exchange fails to find an email address using FromTerm, FromStringTerm, RecipientTerm, or RecipientStringTerm. As described in this blog entry, Exchange will only find a personal name using these search terms. Instead, use a HeaderTerm to search for the email address.
Exchange 2010 has a bug where it returns NIL instead of "" for empty parameter values, causing a NullPointerException. A workaround was added to JavaMail 1.5.5.
Searching for an address in Exchange 2010 matches only the "personal name" field of the address, not the email address itself. (Reported 12/8/2015)
Exchange 365 returns an incorrect BODYSTRUCTURE response for single part messages, failing to include the message disposition value in parentheses as required by the IMAP spec. See this bug report. This causes a MessagingException with the message "Unable to load BODYSTRUCTURE". Use the workaround described in the JavaMail FAQ.
Exchange 2010 has a bug where it fails to quote the encoding value in a BODYSTRUCTURE response. This causes a MessagingException with the message "Unable to load BODYSTRUCTURE". As of 1/10/2011, a customer reported that Microsoft expects to fix this bug in "Roll Up 3" for Exchange 2010. JavaMail 1.4.4 includes a workaround for this Exchange bug.
Exchange 2007 has a bug where it returns "-1" as the size of a multipart/signed body part (at least) in the BODYSTRUCTURE response.. This causes a MessagingException with the message "Unable to load BODYSTRUCTURE". Use the workaround described in the JavaMail FAQ.
Exchange 2007 has a bug where it advertises that it supports AUTH=PLAIN, even though this Exchange documentation claims that it's not supported. This causes JavaMail to choose PLAIN authentication, which will always fail. To work around this Exchange bug, set the session property "mail.imap.auth.plain.disable" to "true". (Change "imap" to "imaps" if you're using the "imaps" protocol.)
On Aug 6, 2012, a customer reported that Exchange 2010 has a similar problem where both PLAIN and NTLM authentication fail for shared mailboxes (with user names of the form email@example.com/sharedMB), even though they work for regular user mailboxes. Disabling all authentication types and falling back to IMAP LOGIN support seemed to work. See this thread for more details.
Exchange 2007 through SP3 has a bug where, at least in some circumstances, it will report a message as a result of an IMAP SEARCH command that it had not previously notified the client of via an EXISTS response, causing an exception such as "java.lang.ArrayIndexOutOfBoundsException: message number (1) out of bounds (0)" from the Folder.search() method. A workaround for this bug was included in JavaMail 1.5.1. (Reported by a user on 6/18/2012)
To access a shared mailbox in Exchange, you need to login using the "alias" name and password for the shared mailbox, which you can get from your Exchange server administrator. This article has more information.
In Exchange 2007 Microsoft removed the ability to access public folders, and they have no plans to restore it.
To access a shared mailbox using Office 365, see this article.
In some cases, Office 365 will accept a bad password for a correct user name and then later return the error "BAD User is authenticated but not connected" for subsequent IMAP commands, resulting in a MessagingException.