What is the best way to upload a PDF attachment, that can be attached to multiple nodes? I want multiple nodes to all have a download link on each node to one, shared PDF file.  

What is the best way to upload the PDF file one time, but add it as an attachment to each of the multiple nodes?  

This is easy to do for one node:one pdf attachment using the File Upload module, but I'm not sure of the best way to associate one single PDF with multiple nodes.
Two approaches spring to mind. Either you keep using a filefield and use something like FileField Sources to select already uploaded files; or you use a file-as-node idea, and create a content type for PDFs, use nodereferences to attach them to nodes, and use something like Nodereference Explorer for browsing.