Theses problems mainly occurred to users with network home directories.
It affected some massively while others had not problems at all.
Even on the same Mac.
In our case this caused mail and calendar to be unusable to those affected.
Updating to that latest 10.9 seemed to help somewhat.
These steps seem to cure the the problems on the other users affected:
- Delete every folder in ~/Library/Keychains that has a name somewhat like for example 'ABF6C3A9-702E-5666-AE78-0D0D96A676BA'.
- Delete ~/Library/Preferences/com.apple.security.cloudkeychainproxy3.keysToRegister.plist
- Delete ~/Library/Preferences/com.apple.security_common.plist
- Open 'System Preferences > Internet Accounts'.
- Select each account and enter the passwords as required
From there on mail and calendars work seamlessly again.