As with most first-person WebGL projects, things go wrong when the mouse pointer leaves the canvas area. Is there anything that can be done to "capture" the pointer (that isn't horribly open to abuse...)?
It's already there. If you run the demo with a dev version of Chrome going into fullscreen mode locks the mouse cursor and gives you more traditional FPS controls. This should be making its way into the stable versions of several browsers within the next few months.
Would it be possible to throw in a server, add a few grains of socket.io and make this multiplayer ? I don't see why not, and it would make it a much more appealing experiment.