I discovered yesterday that my Dropbox contextual menus had disappeared. I have no idea when it happened. It might have been when I installed Mavericks... that's how little I use that feature. But when I need it, it's damned useful.
It took me about an hour of poking around the Dropbox forums (which were no help, ultimately) and trying various queries in DuckDuckGo to figure out how to get the menu options back. Hopefully this post will save others a bit of troubleshooting time.
I should have figured that Rui Carmo would have the answer. Here's what he said:
If you lose Finder icon overlays and context menus, quit Dropbox and do this:
sudo rm -rf /Library/DropboxHelperTools killall Finder
…and restart Dropbox. It should ask for an administrator password to reinstall the Finder plugin, and all should be well.
Bingo. That worked! And (weirdly) it restored my ability to get proper public file links so I could finally find my Dropbox user ID.