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The main challenge with Server Core in Windows Server 2008 R2 and Server 2008 is that Server Core has to be set at installation time and can't be changed without reinstallation.
This is a big risk for organizations not used to managing Windows Server from a command prompt or remotely.
You'll still need to patch and reboot, but you won't have to patch and reboot as often.
In addition, in Server 2008 R2 and Server 2008, Server Core is supported for only infrastructure roles (i.e., roles that are part of Windows Server itself) and not for other applications. Server Core is now the default installation option for Server 2012.
The graphical interface, management tools, and management infrastructure can now be added and removed at any point in a server's life cycle, with only a reboot required.
Rebooting a server typically means the services running on that server have to be unavailable during that time.
This gives you a lot more flexibility and granularity, because you can choose to have the management infrastructure but not the graphical interface, for example.
In addition, Server Core is now an application platform, so applications (e.g., SQL Server 2012) can run on it.