I prefer to use Peoplebrowsr as my day to day twitter/social media client. It has all the advanced features you need to keep track of a large follow count, research and keep many social network feeds in one place. Peoplebrowsr is also great for drilling down on specific users or keywords. Especially specific users in Iran such as @iran_change
The solution I found was Twitterfall. By pointing the Twitterfall search at #iranelections, placing it on a seperate monitor I can have a large feed of all the current tweets that I can glance at to sense a mood for the tweets.
Interestingly a large portion of the tweets are related to #cnnfail. Or CNN's apparent extended delay in reporting the riots currently occuring in Iran. It is clear that the mood in the twitter community is that mainstream media is becoming increasingly irrelevant to them in getting information.
For these kind of events I would also highly endorse that you also use Livestation. Its an excellent Windows program that allows you to stream some excellent 24hr news channels including AlJazeera, BBC World News and Russia Today.
It proves to be an excellent free resource for access to traditional broadcast media channels.
More than anything else I am trying to show that a mash up of readily available tools allows almost anyone to track breaking news to a depth that would not have been possible just a few years ago.
And throwing all your eggs in one basket wont really help. Pulling all three tools together has allowed me to feel more on top of a breaking news situation than I have ever been able to before.
And as for CNN - you seem to be bearing the brunt of the mainstream's media's failure.