It's astounding how fast Twitter has gone from being a digital frisbee, good mostly for one-liners and embarrassment, to a central tool of a people's uprising, of such importance that it could legitimately change the course of human events if it goes down for 90 minutes (and anyone reading this on June 16, write in now and tell them not to freakin' do that!).
What brought Twitter from Ashton Kutcher to Herbert Morrison wasn't so much the service as the technology on which it piggybacks. Someday our phones may all be browsers and our wishes all horses, but right now the most ubiquitous tool for global communication is the cheap-ass cell phone. By allowing for easy sending and receiving via a technology with far more market penetration than smartphones (once again proving that smart is the antonym of ubiquitous), Twitter first became a handy way to tell the dudes that you were gonna be at the quad, and then became the best means for those dodging bullets in Tehran to tell the world what's going on.
Even if the media wasn't so pathetically dropping the ball on coverage, Twitter would still be the best way to find out what's happening right now. Not the best tool for understanding what's going on in Iran---there's no way to know what tweets are just rumor-mongering or disinformation, especially in the absence of visuals---but certainly the best way for those on the scene to do live reporting, and for those interested to see that reporting.
That is not to say that the current GOP Twitterspoogefest isn't as completely stupid as most every idea that comes from the GOP. Twitter is very good for realtime organizing, but the Republican party doesn't need organizing in the sense of "get 1,000 people to meet in the middle of Grozny", they need organizing like "let's get a party leader who's neither a clown, a fraud, or a sociopath." They also need a more compelling message than the one they've got, which they won't find at under 140 characters---that's plenty of space for their current message, but then, that's the problem.