Only email and calendar are affected by permissions. Contacts/Memos/Tasks do not require any special permissions.
For Calendar make sure that BESAdmin has the correct permissions down to the mailbox and public folder store levels in the Exchange Management Tools. Also, BESAdmin cannot be in any admin groups, unless the BES is on a DC. Then the account belongs in built-in admins only.
Also, there is a switch administration account doc for 4.0 and 4.1: BlackBerry Search Results
The one calendar doc is here: BlackBerry Search Results
If reconcilation is not working on your BB check the reoncilaition options on the device, Messages>Options>Email Reconciliation. It should show:
Delete On: Mailbox and handheld
Wireless Reconcile: On
Check the Wireless Sync option as well for any other PIM item that isn't working.
Is this affecting all items or just reconciliation and calendar?