Earthquakes are a poor example. http://quake.wr.usgs.gov/recenteqs/latest.htm is going to give you more timely and accurate data than someone's random tweet.
However, there is a totally different kind of value to Twitter posts: instead of data, I'm getting firsthand accounts of who felt it, where, what they were doing at the time, and what effect it had on their life. Yes, this information is (obviously) anecdotal, but its also interesting, informative and immediate.
And since it's backed by actual scientific instruments, you can tell immediately if it was a magnitude 3 in Berkeley, or a magnitude 6 in Parkfield, which is better than some tweet of "I just felt an earthquake".