How important is grammar and syntax in social media?
Sorry, but I think you're asking the wrong question!
The importance of grammar and syntax is first and foremost decided by who the target market is. Teachers are likely to care more than teenagers if your grammar is not up to scratch.
The second consideration is what you are trying to sell. People are more likely to forgive poor grammar from a plumber or a hairdresser rather than a financial advisor or a lawyer, even when all are selling B2C.
All that aside, the simple rule is that fewer people are turned off by good grammar than by bad grammar, so err on the safe side. Unless of course you are a punk band with a rebellious anti-establishment brand position, or something along those lines...
It is incredibly important. Writing well is a reflection of your intelligence and professionalism. Social media is also public media.
If you want to use colloquial "text speak" among your close friends and family by all means do so, but make sure it cannot be accessed by anyone in the business world.
Even with Twitter, and its tight character limit, it's still possible to write tweets without contractions ("u"/"ur"/"4") and it looks far better.
I'm always staggered how many people have errors of spelling, punctuation and grammar in their LinkedIn profile summaries. Including people who work in communications-related fields, from media to PR & marketing. There is absolutely no excuse for that.
I would say it is very important. Of course we all make mistakes and the odd error slips through (particularly noticeable after we hit the post or send button) but if the text is laden with errors then I am definitely going to take the organisation or the individual less seriously. If you want to look professional regardless of your field, then my advice would be to take care in all that you do and write.
At the end of the day, Social Media is a way to converse with your community. While Twitter is restrictive with the number of characters available (and therefore the audience is a bit more forgiving), I tend to agree with the majority here that bad grammar is bad communication - regardless of your audience. Always put your best foot forward, and find a way to get your message across quickly and in few words to get the cut through.
4 personal use, gramma and syntax doesnt matter, but for PR purposes it is extremely important - because what you post is a reflection of your company's image.