The short answer appears to be "enough to lose your job, but not enough to be informative."
The ever entertaining Gerard Henderson has brought the evidence together in this week's Media Watch Dog when he covered two Twitter events. He gives s the low-down on the incredibly un-sad demise of Catherine Denvey at The Age for her tweets on ANZAC Day and on the Logies.
He follows this with a piece that demonstrates the complete "inanity" (is that a word? If not it should be.) of the tweets received by the ABC's Q&A.
My recent experience has been attending a really good two day policy conference (RadComms 2010) conducted b the ACMA. The ACMA has engaged Tom Burton as their Gov 2.0 adviser. Full credit for web-casting the conference. But they then decided to have a twitter conversation on it as well, including the ability to ask questions.
I know I'm verbose and also use the opportunity of questions to make statements, but I'm not sure I could ever construct a meaningful question in 140 characters on anything to do with spectrum policy and broadband.
By all means support a webcast with a text conversation. But what was wrong with old fashioned chat room structures rather than twitter?
Recently a judge allowed the decision of a court case to be covered on twitter - i the iiNet v AFACT case on copyright. It allowed me a "small moment of fame" when a journalist tweeted "David Havyatt arrives"
Anyway we now know what to do if - horror of horrors - they ever invite Catherine Denvey back to Q&A. Get your twitter fingers ready! What can we say about Catherine in 140 characters. "Get her off - she is boring"?