Oh, please, give me a break.
I would be the last to argue that everything on the Internet is "public" (in fact, I was one of the first pointing out that it is not, see our 2001 paper in the BMJ at http://www.bmj.com/content/323/7321/1103.full), BUT TWITTER IS PUBLIC - NO QUESTION ABOUT IT.

Tweets (from the public stream) are like to be treated like blogs (microblogs) and webpages - PUBLIC. No consent required for analyzing them, unless of course they are DMs (which are like emails - confidential) or sent to your "followers only". The Twitter terms of use are VERY clear in this:

"Our Services are primarily designed to help you share information with the world. Most of the information you provide to us is information you are asking us to make public. This includes not only the messages you Tweet and the metadata provided with Tweets, such as when you Tweeted, but also the lists you create, the people you follow, the Tweets you mark as favorites or Retweet and m...