And yes, a native most often does not speak correct written language, but foreign speaker might. This does not mean the foreign speaker is as good at the language as the native, he's basically got the grips of the guidelines but lacks the skills of creating his own personality through what he is saying.
I do a lot of transcribing of spoken interviews for analysis. Spoken language is full of false starts, corrections, incomplete utterances and interjected non-words (umms and ahs), but I would argue that once you strip all that stuff out, the vast majority of the time you're left with a grammatical statement. So yes, people do usually speak "correctly" (though of course they don't speak in written language, that's a contradiction in terms). Whether or not slang and other informal uses common in spoken language are accepted in the written form is a cultural question, not a grammatical one.
As for a foreign speaker "lacking the skills to create his own personality through what he is saying", Joseph Conrad is one of the greatest writers in the English language, with a very distinctive personal style, and he didn't learn the language until adulthood, and spoke it with a strong accent to the end of his life. You could also add Vladimir Nabokov, though he learned English from a young age. Salman Rushdie's first language is Urdu. So no, it's not impossible.
Eh? I'm on the same corridor as a computer linguistics department, and I can assure you based on the research posters they hang up (I remember one in particular that was looking at Swedish TV subtitles) that academic researchers are still working on computer translation. Besides, computer translation plays an increasingly important role in the real world, with tools like Google Translate (including on YouTube subtitles) and Word Lens for the general public, and special apps e.g. for soldiers in Iraq.
What I meant by the academic community is not the same what you're referring to as Google or Word Lens, which two are obviously products of companies rather than university research.
Well, like I said, my office is on the same corridor as a computer linguistics department (i.e. at a university), and they do still work on computer translation. Besides, most of these cutting-edge problems in computer linguistics and AI are collaborations between university research groups and companies (or government agencies like DARPA).
Anyway, the fact that a computer translation can never be correct renders the whole area of study useless, which is why it's been mostly abandoned. But as said, this polish researcher for example never gave up. And who knows when it'll come back. It just doesn't happen now with what we've got.
Right. Just like how the fact that we can't achieve eternal life renders the whole discipline of medicine useless, which is why it has been mostly abandoned.

"there are as many languages as there are speakers". Meaning we all have our sociolects etc, children speak differently, everyone has a different register when speaking to his boss or his brother or best friend etc.
So how can people communicate at all, then?
Do you not understand any other languages than your own or even any dialects of your native language? Speak with a child about politics and you'll see what I mean. at the same time, it's easy to spot social classes from each other through word usage and pronounciation, and a lot of people choose their company according to what and how they speak, be it, that they all use the same guidelines and grammar.
My point was that the fact that communication is possible at all means that there is a certain shared understanding of terms, a commonality in language. Or maybe you would prefer "The fact that one person trying to understand another can never be correct renders the whole concept of language useless, which is why it's been mostly abandoned."
Of course most of it is understandable, seeing as the original text is most often available. But a translation is worthless if it doesn't give out the exact message the original one would, and by this I mean translating literature, not separate sentences of correct grammar.
I'm... I don't even...
That's not even wrong. That's
insane.
It's impossible for a translation of any particularly challenging text to "give out"
exactly the same "message" as the original. So does that mean that all translations of the Bible, all translations of
The Iliad and
The Odyssey, of Beowulf, of Dostoevsky, of Kafka, of Asterix are worthless? Any movie with dubbing or subtitles, worthless?
You're a translator, right? So your job is being worthless, I guess?
Let's be a bit more specific about "worthless" computer translation:
I sometimes find websites, e.g. Wikipedia articles, that are only available in languages I don't know; but I can run them through Google Translate and (with some effort) read and understand them. That's not worthless to me.
I often get emails in German that would take me maybe ten minutes to interpret. With a single click, Google Translate gives it to me in English. Even if the sentences aren't elegant, or even all grammatically correct, it takes me a fraction of the time to understand. That's not worthless to me.
I have friends on Facebook who are Dutch, Israeli, Greek, Finnish, etc., and who sometimes post in their own language. But since Facebook added a translation feature, I can just click to see it translated, and even if it doesn't always work perfectly (or sometimes even at all), it's often good enough for me to know what they're saying. That's not worthless to me.
I've used Google Translate to help me read comics in French, since it's often quicker and more helpful than a French-English dictionary. That's not worthless to me.
I also have French books that I have scanned and run through OCR. I can do searches for particular key words, and auto-translate the paragraphs around each result to see if it's relevant, narrowing it down before I send it to someone who can do a more accurate translation. That's not worthless to me.
As recently as
this morning, I was carrying on a correspondence with someone in a language
I don't know. I'm sure my Google-translated messages had lots of mistakes (though I did try to verify them using some of the methods monkey mentioned, as well as others), but we could communicate. That's not worthless to me.
I can use Word Lens to help me understand signs when I'm on vacation in a foreign country. That could stop me from getting lost, help me select what I like from a menu, help me use a ticket machine... it could potentially save my life. That's not worthless to me.
Thinking that a system has to be perfect or else it's worthless blinds people from the huge impact that "good enough" computer translation can have, and already is having. There are things it's still not good enough for, given particular requirements (and alternatives being available), sure. But that's a completely different claim.