I have been blogging before about privacy: privacy is not about what others (might) know about you, it is about something different: One of the mechanisms you use to influence how others relate to you is by determining what information others have about you. The context of the information is everything. Privacy is violated by using information in a total different context, by creating a different relation by it. So in a personal setting you might say: "I will blow the airport sky high", just to express your anger, while you know that saying that at the airport security is a bit of a different context where you relate a bit different to the people present...
So what if you say exactly that on twitter, like Paul Chambers did? Twitter is mostly used for personal messages. It is not the place where communicate to security officials. So the messages you send should be interpreted, and kept, in that context. Unfortunately that is not what happened to Paul Chambers, as everybody knows. His words where meant for the private realm, where part of the personal relations he maintained by twitter. Prosecuting him for twittering "I will blow the airport sky high", is taking his words seriously out of context and abusing those words are meant for.
Apparently there are people constantly looking on media like twitter for tweets like these. And apparently they think they should act on tweets like these. Twitter is personal and if you take that to court like this, you are violating privacy. Stop that, or I will blow you sky high.