One issue: because editing and saving is not live there were some issues, namely that we had to coordinate who was using the document when. We ended up with several conflicted copies and extra work.
We're currently trialling it for corporate templates (Coaching Programs, Project Documents etc). Point their MS Office to a Dropbox folder, and every coach in the world will have the latest templates all of the time.
We would benefit from some permission levels (read, no write etc) to make sharing less of a risk for a bigger team, however. While it can be unwound, one person accidentally changing a template could go unnoticed.
I didn't dig too deep, but when we let someone go, we'd prefer that they not be able to access our private files anymore. (Especially when they go to work for a competitor!)
If you're still worried, change the password every time someone quits. (Which is usually a good idea.)