what error code do you get on the machines where it fails?
Given the syntax you use, I don't think you've mapped any drives but are using the UNC syntax so mapping should not be an issue.
If it works on some, but not others, it could be an PDF browser plugin issue. Try to open the PDF file directly in the browser on one of those problematic machines. That will not only ensure that Adobe Reader (or some other PDF reader) is properly set up to view files in the browser, it will show you the exact path in the address bar.
Then make sure the Open URL dialog is on so you can se the exact URL being passed to the browser.
use of file:, filemac:, or filewin: may be needed here
You can use a case statement to determine the platform.
ust to make it clear, I'm opening the enclosing folder, not the pdf files...
file: URL starts with 3 slashes, then write UNC path using slash
or file: is opened by Explorer on Windows, so write UNC only using back slash.
in text literal writing 4 back slashes become 3 back slashes when saved.