Dropbox has a new "Fix Permissions" feature
If you get "Permission Denied" errors, you can try to "Fix Permissions" in Dropbox. This is not repairing disk permissions in Disk Utility, it's within the Dropbox app itself.
To get to it, open Dropbox preferences, then click "Account" and you'll see this:
Make sure that "Unlink This Computer" is highlighted (if it isn't, press Tab until it is).
Hold down the alt/option key and it will change to this:
I assume this is a new feature in Dropbox version 2.
If you're not reading Mac OS X Hints already, you really should start.
Fix Dropbox permissions via Preferences » Account and hold down Option/Alt.