>...then users could have a web site up on their smartphones scan the barcode and be told if their document was the up to date revision.
Well, you can embed whatever info into a QR code, so that would be a link like
and a script could then tell the user if xyz is the current version or there is a newer one. If you need to modify a pdf to include a page with a QR code, you could also put in the link, much easier, if a user reads the pdf at a computer or reader. If a pdf is printed, an accompanying QR code could make a user having a smart phone at hand check the document version without a pc, reader or scuh device, so the overall idea is plausable.
Visiting a link embedded in a QR code is a standard action triggered by a QR code decoding app. At the link you embed you can simply return yes/no or in case of no a link to the newer PDF version.
Overall it looks like combining paperback with internet. With magazines pointing to more detailed and up-to-date info that's not unusual, to determine a doc version of a file, you could rather use the file version attribute or cause an automatic update, when a doc is opened, like with an application. I don't know if that sounds better, but it would be possible to put the newest version of a pdf at some constant link and make a (self extracting) executable loading that newest version for display.
In the shortest form, that solution would simply be a constant link to the newest document version itself. A user doesn't need anything else but internet access to open that newest version, which seems to be the outset, if you want the QR code to tell them, if they got the newest version. That needs to be queried at some web page, so a user needs internet access. Or how do you want to determine that? You could embed "this is the newest version" into the QR code, then a user would always be satisfied

That's as up to date as the date printed on a newspaper. Correct for that date.
Bye, Olaf.