I have come across another reason why Windows will not install assigned programs in a Group Policy.  It thinks they are already installed!  I have had a few instances where a program was not installed and I could find no errors in the the event log files.  When I checked the registry there was already an entry for the program indicating that the program had already been installed via Group Policy.

Resolution

Open regedit and go to the following path
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Group Policy\AppMgmt

One there you will find an entry for each program you have assigned through Group Policy.  Find the entry for the program that you are having the issue with and delete it.  The computer should attempt to install the program again once the computer is rebooted.