The BBCheck utility was not publicly posted when I left RIM a few months ago but it does exist and don't worry if it doesn't display all the information, it hasn't been perfected yet.
One-way calendar not working from BB to Outlook is a BES issue. The fixes have all been listed here already.
Typically cdo.dll is a lower version on the BES then the Exchange server. To confirm just search for cdo.dll in the BES MAGT log, if you have multiple either one will do. That will show the registered file location and version. MAKE SURE it is not lower than the Exchange if so apply the appropriate EXCHANGE service pack or just copy it from the Exchange server and register it in the Exchsrvr\bin folder.
If cdo is not the issue then it is most likely permissions. The BESAdmin account CANNOT be a domain admin or an admin of any kind. This revokes the Send As permission used to for Calendaring. The BESAdmin can only be in the built-in admins when the BES is installed on a Domain Controller, that's the only exception. If the BESAdmin is not part of any admin groups then check for the Send As permission in Exchange System Manager. Verify it is set at the server, mailbox store and public folder store levels.
It has to be one of those, that is what the Calendar relies to function properly.
Review this BB article for the issue, it has everything listed here: BlackBerry Search Results