Not every file. It seems only files saved to the Desktop. If in the Save dialog I create a new folder, the new folder does not appear.
More accurately, the saved or created items eventually appear, typically a minute or so later. I can force them to appear by relaunching the Finder.
When I try to Rename a Screen Shot, the new name does not immediately appear. But it will appear a minute or so later, and can be forced to appear by relaunching the Finder.
As per your advice, I tried Safe Mode. The same problem persists in Safe Mode.
I've got another account that I've used as a test. The problem does not persist when I boot up into that account.
Thanks a bunch for your help.