Applejack is a utility that scans your OS X system and fixes things like permissions and file system errors.
It has a mode called “deep scan” mode that seems to break Parallels Desktop’s SmartSelect mode.
With SmartSelect, you can right-click on a file on the OS X desktop or file system and open it with an application running on the Windows virtual machine.
After running Applejack’s deep scan, I found that this feature no longer worked.
The solution was to re-install Parallels Desktop. Fortunately, this was a non-destructive install as it does not require you to remove the previous installation.