Publishing from the Facebook App has the same privacy issues as from the web.

Privacy on the Mobile App:

The first thing to do is always check the privacy. The mobile app will default to the last used privacy as does the web portal.

Simply click the down arrow next the current Privacy setting logo:

Thus, you are presented with the same options as per the web portal.

Simply select the ones you want.
The only real limitation is that the Custom option is stuck/fixed to the last setting used on the web portal. Very annoying!