Now that I'm done complaining about everyone else's Everything ideas, here's one of my own:
Connect to every single webcam and video surveillance camera on earth, and present the images on a single wall -- where a single security guard can watch the god's-eye view and report problems to the Secretary General of the U.N., Dick Cheney, or whoever runs the world.
The bad news is: the guard would fall asleep before scanning a tiny fraction of the videos.
The good news: all those video streams can be stored and pulled together by computer to build a virtual reality approximation of our world. And though it won't do us much good right now, it is the perfect way to build a real Time Machine that people of the future can use to visit the world of today. Note that there is no real limit to the detail that world can have -- it's just a matter of time, energy and computing horsepower.
(If you are going to think stupid ideas, why think small?)