I've found it also good for real time updates. For example during recent snow storms, following the city and department of transport Twitter gives some insight into the status of the city. And they use it for two-way communication as well.
Other situations I've used it is twice watching parades when there was a huge gap in the middle. Jump on twitter and there's reports of why the parade stopped (medical emergency).
I've also used it when following a manhunt that had a city on lockdown. Closest to second by second updates. First there were reports from people listening to police scanner that the suspect was apprehended, and finally the police twitter confirmed. Long before any online news articles.