This is actually an incredibly good idea.
1) Twitter is an extremely popular tool. It's the shortest, quickest, simplest way to record almost all of modern humanity. You might think blogs, or something else, are the better way, but those are too large to collect every singe one. Twitter is a simpler service that would take up less space.
2) This is about the first time in history when we possess the technology to record the histories of ANYONE for historical storage. Before, we only had what remained, or what survived. This will be the first generation in humanity where EVERYONE will be on record.
3) Everyone on record, for better or worse, will provide valuable insight. Even the worthless stuff such as "epic burrito" will be recorded.
AND IT SHOULD
because I, as a future historian, would much rather have boundless information of ranging quality than none (or worse, "selected" that represents out society). Using search engines (which I'm sure will be implemented), historians and sociologists will be able to look up how almost anyone felt about any subject.
4) So if Global Warming really does fuck up our planet, or Obama messes up, a classic movie is made, or anything else happens. People can look back and get BOTH sides of the story, not just the one that history's victor wrote. (so if future people thought we were stupid for liking AVATAR, we can prove them wrong with historical documentation)
5) I'm seriously considering setting up an account now. I still think Twitter is stupid. But I think my own little contribution to the sociological development of my generation is too important. I'm not gonna let it run my life, but I would like my life (even just the smallest part) to be recorded.
6) You can bash it all you want, but do YOU have a better idea on how to record the thoughts of people in today's world for historical services? To be honest, I think this is almost as good as the Census. And if you don't like it, let's see YOU do better.