I'm adding a response here to help folks who may have run into the problem I was having. I upgraded my Windows 7 Pro to Windows 10 Pro and for the longest time after the update I kept running into installation/upgrade issues with various applications including iTunes, Skype, etc... The event log would show that the installer errors out for various but one of the common errors would be 1603 or 1602 etc... I was just living with an older version of iTunes. The problem seemed like some sort of permissions issue but I don't fully understand Window's permissions on the various folders.
So searching around I ran into this tool from the www.tweaking.com to repair a windows installation and so I downloaded their free version and ran it and to my surprise it fixed the problems. The program runs a bunch of different Microsoft tools to fix-up your Windows installation and some of these tools take a while to complete. I think on my system, the tweaking program ran for 2+ hrs in safe mode. But one of the areas it "fixes" is to set all the default permissions to the various folders (Program Files, Windows, etc...). I don't know why my system was messed up and can only assume it was the "windows 10 update" that didn't handle things well but the tweaking tool fixed it for me and now I'm able to install all of the problem programs.
The tool is also real good at telling the user (and providing an interface) to 1) backup their registry, and 2) create a save point in case things go badly.
"Tweaking.com - Windows Repair" at www.tweaking.com
p.s. I'm not affiliated with the tweaking folks and I'll point out that the free version of their tool fixed my problem.