It’s possible to control the public/private visibility of your goal data and fine print using the ‘public’ checkboxes in the settings. It would be nice if the goal page showed you what the value of this setting was without needing you to visit the settings page.
I suggest adding a note about the status next to the heading, something like:
Recent data (this data is public)
or
Fine print (this text is private)
Personally I’d also like to not have to seek out two checkboxes every time to make 'em private. Or, dare I say it, make them private by default? You can pry my irrational secrecy from my cold dead hands!!
The shading on the goal overview page is usually enough for me. I actually really like that the default is public because it makes it a lot easier to learn how to use Beeminder by seeing other people’s stuff.
Haha, nice. I hadn’t even spotted that 
There could be an argument for adding your preferred privacy setting to the ‘goal defaults’ page. (Ideally after changing them to only apply during goal creation.) #XUVI
I’m with @drtall though: there is value in writing your fine print as though it’ll be read by others, and exploring people’s goal galleries. Equally, sharing how each of us handles different cases is a huge value provided by the discussions in this forum (thanks to our ridiculously awesome users).
I’d like the ability to make goals start private by default too.
All my goals are private right now (though I’m a little concerned about this supposed second checkbox. What’s that?). This is likely to continue to be the case.
A thing that makes me slightly… not so much paranoid as “If I were really concerned this would be my threat model but it’s mostly a theoretical curiousity for me” is that hypothetical-stalker-who-I-am-trying-to-conceal-information-from can essentially scrape my list of public Beeminder goals with a script repeatedly refreshing the page, and thus can get information about what goals I’m creating in the period between creation and clicking private.
This is not a very important threat model even if I did care, but the information leak annoys me.