Yes, it acts as a snapshot of society at the turn of the 21st Century. It's as much about social responses to events as it people getting to grips with social media. It's too early to dictate the difference between the mundane and the useful at this early stage. If Twitter had been around in Victorian times then who would ever say it wouldn't be interesting to mine that data?
Twitter is useful as a base for sentiment analysis research. Archiving all tweets would allow direct public access to the corpus of all tweets for any desired purpose under the FOIA, meaning such research would no longer require long collection periods, as currently no such corpus is publicly available. Such tools developed from the availability of such a corpus would be quite valuable to humanity.
Twitter has become part of our culture, and it is a way of seeing what people talk about and how they share news. It would be good for future generations to be able to look back at what we talked about and learn from it, even when some of the content seems trivial. It will not be that costly to archive tweets, so it seems worthwhile.
Most of the tweets are useless, anyway. In any case, sites like HotChirp.Com archive the trending, and thus the most useful and memorable, ones. Archiving HotChirp's posts, and/or the top tweets directly from Twitter, might make sense, but archiving all of them, when 99% of them are spambot junk, would be a waste of resources and would create a database that even the future might find challenging to navigate.
I don't think the Library of Congress should archive all of that nonconstructive crap. What a waste of time. Can you imagine future generations looking back and saying "Wow, grandpa. Your generation was cancerous." If the government really wants to archive culture, they should scour the internet for revolutionary internet projects like the early versions of "Minecraft" as well as homebrew projects like "Axles and Alloys" and archive those instead. That's where the true culture is, in original works of art.
What a ridiculous waste of time and resources. Some great things have taken place on Twitter, but do we really need four million variations of "eatin sum skittlez xd" filed away somewhere? I can't for the life of me understand the purpose of this unless they're just trying to prove they can do it, in which case it's still stupid.
While there is definite benefit to looking at trends on twitter during certain events, archiving all tweets would be a useless, pointless endeavor that would just waste time, money, and manpower. It would be better to archive certain things, such as trending topics, that give an overall view of what people are thinking during a time.
No, archiving all tweets will be a huge waste of time and money. If fifty years, no one is going to care what Paris Hilton had for dinner, or who Kim Kardashian is marrying this week. The vast majority of tweets are silliness that will mean nothing in a year, so why would we save them forever?