Somebody regularly uploads new PDFs to his web page and updates the old ones. I do copy them to my hard drive, however, I am unfortunately not notified of any updates to the files.
Can save a table which maps paths to local files to URIs, from which they were downloaded.
The mapping is supposed to be entered manually, of course.
Regularly checks if the local files still strictly equal (e.g. by hashing) their online counterparts and notifies me of any changed files.
The kind of notification can be arbitrary, e.g. in the taskbar notification area or via a standalone window.
Is able to delegate both the local and the remote file to a diff program, which I can state in the settings.
The update checker would probably download the remote file to a temporary location and the call the diff program with
[path to local file] [path to temporarily saved remote file]
Price: Free & open source is preferred, but I would pay up to 10€ nevertheless.