I think the problem lies in the fact that, in truth, writing well is not at all easy but given the number of blogs, tweets, celebrity ghost novels etc. everyone thinks they can do it.
20 years ago when Pagemaker came out everyone though they were layout artists, Photoshop made them graphic designers and now twitter makes them authors.

Wow, I sound like my dad!

Grammer’s primary purpose is to remove ambiguity from communication, and with more people using written communication rather than verbal it is likely that grammer has improved significantly.  Verbal communication has the advantage of never having spelling mistakes, and gestures and tone can aid the understanding of poor sentence structure or use of language.  Text communication requires stricter adherence to grammatical rules to achieve a similar level of understanding.

Perhaps comparing the number of grammatical errors a 1980s Encyclopedia Britannica and Wikipedia would provide an interesting insight into the development of grammer and spelling in the “internet age”.  

As an aside many great authors throughout history have used abbreviation, abbreviation is not a sign of a reduction in the quality of communication, it is more likely to do with a limitation of the communication medium.

Most of the examples you site seem to come from social media. It’s important to note that many of these communications you sited are very casual. Social media in particular is geared toward short expressions as opposed to long discourses. Take twitter for example. The 140 Character limit makes brevity a necessity. In these cases we often write like we talk in casual conversations. We often use slang or euphemisms when chatting up friends. Now, I’m not making excuses for poor grammar, but I do believe that context is important.

I agree that grammar will continue to be important. As for the case of the newspaper article, clearly this was laziness on the part of the writer and editor (I assume this was a college newspaper?). They clearly did not take the time to review, edit and research proper format before publishing the article. This brings up another interesting discussion…the ease of self-publishing.

Just about anyone can publish themselves anytime, anywhere. The prolificness of blogs, smartphones and social media makes it simple and fast. That means the amount of content that is available at our fingertips is growing exponentially everyday. Most of these new publishers don’t hold to the rigorous editorial standards of traditional publishers. Hence, more public examples of poor grammar.

There are appropriate places to use text grammar such as social media sites and text messaging. Then there are places where you should not use text grammar such as academic papers. Blogging is a whole different form of media. The blog page depends on who or what you are representing. If the page is just for family and friends, then I see nothing wrong with using text grammar. However, if you are representing your company or you are a writer, then text grammar should be thrown out the window.

There are two questions you should ask yourself before writing anything. First, who am I representing in this document? Second, who is my targeted audience?