It's interesting and it's been going around for a while, including others in the "Did you know series." Always thought-provoking, and I've mentioned before that it's really hard to get our heads around the implications of exponential change.
That said, I do believe it's possible to be too glib.
Exhibit A: "There are 5x as many words in the English language as in Shakespeare's time".
Okay, but I believe that Shakespeare still has the largest vocabulary in his corpus of any single published author in history. What is not mentioned in the video is how much knowledge has been lost, both in terms of crafts and in terms of the large number of languages that have died off. So yes, many technical terms have been invented, but I wonder, are there more unique words in England now than then, what with most regional languages and dialects having died off since Shakespeare's time?
Exhibit B: A week's worth of the New York Times contains as much information as the average person was likely to come across in the 18th century.
What possible definition of "information" is at work here? I could as easily say "The average person takes in as much information in the first 20 seconds they are awake than is contained in an entire week of the New York Times."
Exhibit B: "Half of what they learn their first year will be outdated by their third year"
Only if their curriculum is poorly designed as in "computer classes" that do things like teach "Adobe Photoshop CS5" courses instead of "Principles of Visual Design" courses. On the other hand, UC Berkeley, sometimes considered the best CS program in the US, doesn't even have language courses on the curriculum. If you need to learn C or Java or Python, you have to take self-paced courses to learn the language and as a CS major I don't think you can even get major's credit for them beyond the first one. They believe that a CS major learns how to learns languages (among other things) rather than learning languages themselves.
Exhibit C: "By 2013 a computer will exceed the processing power of the human brain."
Maybe, maybe not. In the 1970s, people thought computers were a decade or so from learning natural language. Given how little we still know about the human brain, I find it doubtful we'll see a computer that can truly out-think a person (meaning everything from chess and Jeopardy to actually being able to do that *and* drive a car, write a novel and and and). I believe it may come some day, perhaps even 2023, but not by 2013.