I don't have a source for Google's original mission, but I think it is fair to say that their current mission is to collect as much information of all kinds as they can, make it findable by people, and make money by selling targeted advertising accordingly.

If Google make their products more social then their is a clear value-add for the consumer of the data, and also a value-add for advertisers. I don't think Page is making a mistake here at all.

Google's original mission was predicated on the existence of Web as it was in the late '90s. Doing just what they did then is not an option, and it's not merely because they've grown.