There have been several cases of late where people have received convictions for what they have said on twitter. BBC Newsbeat has talked with Attorney General Dominic Grieve, who has said that no new laws are needed to police social media networks, as there are already laws that cover material this area and make it illegal to 'grossly offend' or 'cause distress'.
The example is used where tweeting, or posting to an online forum is akin to handing out pamphlets in a pub, that contain the same offensive text. The example seems fairly reasonable, as while many people see twitter as talking face to face, when posting a tweet that is not a direct message you are allowing the public to read what you have said. Obviously what people say in a direct message, or private email is a different matter, which is more like a private conversation you have in your own home.
The issue itself is not new at all, and has existed since the very first dial-up and university bulletin boards existed, the difference now is that the potential audience is many times larger.