My twitter account settings are set to pulbic view, which means people who don't follow me can see/interact with my posts. However I have hidden my birthday and location when I do post unless I specify. Generally I only specify if I am at landmarks like Mt. Rushmore or a sports stadium. I only allow some data to be collected by Twitter (most related to Ap functions/crashes).
That is a good point about what information you allow Twitter itself to collect. I don't post hardly anything online for others to see, but should pay more attention to what I may be giving away to the site itself unwittingly.