Anybody else having trouble with Microsoft Office 365 on Mac OS X 10.8.2?

I've set up two separate Office 365 accounts for two separate clients and configured multiple users in each account. All users are on Mac OS X 10.8.2, and I configured each account the "Mail, Contacts & Calendars" module in System Preferences. The set up process worked flawlessly.

Additionally I've set up each user on at least iOS 6 device (most have both an iPhone and an iPad, however). Again, I set it up using "Mail, Contacts, Calendars" in Settings.

There are a fair number of problems that all users are having with Office 365, but the most disruptive one is with mail. Users report that they can see some, but not all, email messages on their various devices. Testing indicates that if a message is initially received on one device, it cannot be viewed on others. For example, if a message is first received on a desktop Mac, it is not visible or accessible on an iOS device; conversely, if a message is first received on an iOS device, it is not viewable or accessible on a desktop Mac.

Are there any other people out there using Office 365 with Macs and iOS devices having problems? Conversely, are there any other people not having problems?

Also, I'm wondering if is aware of a way to "force" either mail client to sync with an Exchange server