How to reference identical files on multiple nodes?
One way to do this is to use the Media suite which provides a media browser from which you can select existing files. Media also allows to add fields to your files to add additional meta data to them. The current UI in Media 7.x-1.x is unfortunately not what you could be, there are e.g. no filters in the media browser.

An alternative, as suggested in the comments, is to create a content type with just the uploaded file and then reference that node instead of the file. I'd say this is more the 6.x-like way to do this, but it does work as well...