Those are just minor implementation details. Off the top of my head, the key can be stored as a password protected file inside the Dropbox account its self, synced like any normal file, but perhaps hidden from the end user. The encrypted folders contents are synced like any others. On any client where you want to access the decrypted folder contents, you'd just enter the password to decrypt the password protected key and the folder contents would become available. If you forget the password then you're screwed.

The only way Dropbox could access those files then would be to backdoor the Dropbox client. But if they were going to do that, it wouldn't even be safe to use TrueCrypt or GnuPG either.