A map of languages used on Twitter, with more breakdown at FastCo.Design
The default answer to the above is surely "making it worse." When it comes to social networks, grammar, syntax, spelling, and all the rest of it give way to decomposed bites of, hopefully, meaning. If meaning is sustained, what difference do the materials make? Just the other day my dad was ripping on me for using bad grammar in a text message (note: it wasn't that bad), with my reply being something along the lines of, it's just a text message.
I don't really believe that answer, understanding well enough why rules of language exist, but that worry dominates most of the conversation about language and social media, and even digital communication in general. There are other, more interesting possibilities for language in the new world.
One of those is the possibility of rapid language fragmentation, or new online subgrounps generating new languages or language variants. So, rather than the many hundreds of years it took for all of the different languages of the Germanic people settling Great Britain to melt together into English, we have very fine-tuned communities coming together in zero time, relatively speaking, and spending tons of time communicating with each other online.
So, you could view our current situation as language evolution in fast-forward, and now it seems that we have some proof. A trio of researchers led by the University of London's John Bryden has a new paper out suggesting that, based on language analysis, Twitter users are separating into communities (the Guardian says "tribe," rather unforunately).
In the author's words, "... we were able to predict the network community of a user, a purely structural feature, by studying his or her word usage, and we found that this was possible with rapidly growing accuracy for relatively few words sampled."
So, based on things like word length, words, and word-fragments, the team was able to pick out which online communities were which, or even that those communities exist. No hashtags needed. Most of the paper's discussion has to do with information/belief spread and community identification--and new, better ways of doing so--and less so with language development, but it's interesting to consider Twitter communities in the more distant future and what they means for words. I can think of obvious anecdotal stuff like 4chan slang or whatever, but this seems to suggest something more natural.
If we can pick out online communities--perhaps so-far undefined communities--by the words they use and how they use them, define them by language, it would seem those divisions should influence the development of that language.