C:\Windows\system32>dism.exe /online /enable-feature /featurename:NetFX3 /All /S
ource:D:\sources\sxs /LimitAccess
Deployment Image Servicing and Management tool
Version: 6.2.9200.16384
Image Version: 6.2.9200.16384
Enabling feature(s)
[==========================100.0%==========================]
The operation completed successfully.
C:\Windows\system32>
.NET is now installed. I don't know why the original installation method does not work or when or if it will be fixed but this is good work around for now. One positive feature of this method is that the installation can be run offline.2012-12-13 10:28 UTC
For some reason it is not possible to install .NET 3.5 under Windows 8 the usual way by going to Programs & Features -> Turn Windows features on or off. The system will try to connect to Windows Update but will fail with a rather cryptic error code. There is however a solution. It can be installed offline from the original Windows 8 installation medium via a command line utility dism.exe.
Insert or mount your installation disk and run the following command. Replace D: to match your own drive name.