I also couldn't add users to the farm administrators account - I would get an odd exception - "Local administrator privilege is required to update the Farm Administrators' group."
I tried rebooting, uninstalling, reinstalling to no avail - the same problem persisted.
There are many recommended fixes for this problem - most of which didn't work for me:
- Run in an alternative browser such as Google Chrome/Firefox - this didn't work for me.
- Ensure that the Application Pool account in IIS has the correct database permissions - this wasn't the problem in my situation as the user was a full local administrator and sysadmin on the database
- Ensure that you run IE as an administrator - this is already done by the default shortcut to the SharePoint Central Admin (I wasn't opening up SharePoint Central Admin from a seperately instantiated browser - so this also wasn't the problem)
- Ensure that UAC is turned off as this somehow interferes with the application of security to those controls. Most references to this indicated that this worked for Windows 7, but there was no reference to this working for Windows Server products.
Control Panel - User Accounts - Turn User Account Control On or Off
After the reboot, the controls were suddenly re-enabled. This is not a recommended configuration - but this was purely for demonstration purposes rather than being a production-ready install (we would be using Active Directory for that anyway).