Hi James, I think people ought to know that they are not as anonymous as they think on Twitter (or the internet) in general. To remain anonymous, you must never make a mistake: a single post containing identifying information (photo, location, workplace/etc) is enough.
I was shocked when I made the discovery: 'Doxing' people is surprisingly easy (especially with the tendency to reuse same handles on different services, Google image search). It's really a fascinating area, e.g. it's possible to give a good guess on authorship by using software that analyses your writing style/word choice, given input text of a sufficient length.
A good rule of the thumb is to assume what you do/say online can/will be traced back to you, IRL, even though the probability of someone to be sufficiently motivated to do so is rather low.