Thanks for the observations. It appears to just be a problem with Adobe PDF files on my machine. Adobe Reader XI is my default PDF preview handler. It doesn't appear to want to let go of the file if I have a preview in the preview pane and try to delete it. I've tried this with files of other formats and do not have this problem.
UPDATE:
I uninstalled and reinstalled Adobe Reader XI and got the same behavior. Then I tried the Lenovo Reader software that came with the machine, same behavior. Then, on a Microsoft Community thread, I read a discussion on a similar issue and someone recommended trying the free version of the
PDF-Xchange Viewer software. I installed that and made it my default PDF viewer, so it took over the role as the PDF preview handler. Now I can see previews of the files and then delete the ones that I do not want without any issues.
Not really an ideal solution, but one that works for my problem. Is it a Classic Shell issue? I don't have a comment on that as I do not have another Windows 8 machine in the house to use for alternate installation tests. I will leave this thread up though in case someone else runs into this problem and it can be better pinpointed if it is related to Class Shell or is more generic.