The answer to the Right Click Problem!
If you right click on the START button but do not see a context menu you likely have corrupted or missing folder:
c:\User\<user>\AppData\Local\Microsoft\Windows\WinX
The solution is just to copy this folder (and its three subfolders) from a working machine. In my case, I was able to copy these files from a different Windows profile that was not experiencing the problem.
Also, in case you have not figured this out yet, you can customize your right click menu by making changes to:
c:\User\<user>\AppData\Local\Microsoft\Windows\WinX\Group1
c:\User\<user>\AppData\Local\Microsoft\Windows\WinX\Group2
c:\User\<user>\AppData\Local\Microsoft\Windows\WinX\Group3
I used a user I'd set up as a trial and not worked with. Looks like Default would be a good bet too. This helpful tip worked to deal with the problem and there are some useful bits of info in the responses to the fix
which you can find here.
My system is still behaving strangely - programs seem to be losing preference settings and opening like it's the first time and I've found at lease a couple that are missing completely from the start menu, both tiles and the listing. I'm just going to deal with things as they arise and hope that a future update will sort things out.
I did do a backup with Macrium and it looks like it's going to be my tool of choice from now on (although I still need to test with a restore). Many thanks to davehc for his help with this problem.