Laughing because I don't have FB so haven't played with the interface, but there is a 100+ long thread in the Meta Questions section with people posting about privacy concerns. I don't begin to follow it as I am not a FB user, but can tell you how the system is set up if that helps!
How these buttons to Twitter, Google+ and Facebook are supposed to work, is that you are logged in here and logged in there at the same time (to make a connection). If there is a thread that you want to link to your Facebook page to share with people, you click the Facebook link here at DU and it is supposed to send it over there. Noting that it will send a link to the thread here you linked from, not an article in the thread (the news sites have a FB link for their articles seperately).
The only caution I would have in using it is that your FB people may be able to figure out your DU user name if you post enough stuff that you are commenting on here (at first, it will just look like a link to a DU thread, but after enough of them, people may make a connection), so if you have concerns about keeping your DU and your FB lives separate, you may want to be careful with that one.
As best I can tell, the privacy concerns are (i) people's DU IDs being outed in their FB accounts and (ii) FB tracking you everywhere you go on the web if you don't log out of their software, but that second one isn't a DU problem - it is a FB one. You will need to be logged in both here and there for the connection to work.
Given that it is late at night now (1:30 my time anyway), now would be a good time to test it out to see if you like using that option, so you can delete from your wall while people are offline.