I think the most important thing I got from the Web Squared article was the idea that converging information shadows can create a consolidated image of a concept. If you collect enough anonymized information you can not only de-anonymize that information, resolving it to the entity the information is about, but you can form an understanding of the the entity or idea from contextual cues.
Data mining and metadata mining can produce a more comprehensive picture of an individual's life than the individual could voluntarily provide, can tell you more about a location than a hundred tourists who visited on vacation, can explain more about a concept than anything short of an expert on the subject. The metadata becomes semantic information, explaining the character of the entity - when Netflix creates a category for you, it's really more thoroughly defining your tastes than you would probably be able to articulate. You like surrealist goofy 80s coming-of-age comedies? Netflix knows this, based on your ratings, even if you don't.
I'm interested in the production of intelligent agents - expert systems tuned to the individual which know what you like and aggregate information for you, pointing out the things you'd like. Eventually a system like this could be tied to an augmented reality technology, whether realtime (via some sort of monocle device) or offline (giving you a summary of the stuff you saw or missed during the day that is of greatest interest to you). This is something I'd like to eventually be involved in creating for a living.
The most exciting web-enabled application I've seen this year has got to be the Wolfram Alpha Android app. Here we have an application that can solve complicated problems from spoken input.
The last three questions I asked it - out loud no less, requiring no keyboard output - were "What is the average distance from Earth to the Andromeda galaxy?", "What is four miles of water column in atmospheres?" and "what is twenty thousand leagues in cubits?"
All of these would be difficult questions to answer in hand-math, essentially impossible questions for most people to solve as head-math and hard to find the answers to using conventional search technologies. And yet using spoken word data (through a web-informed speech recognition engine) it discovers what I have said, then with a mathetmatically-weighted semantic search engine, combs through its vast collection of numerical data and comprehensive knowledge of unit conversions to provide me with a meaningful answer... most of the time.