This thread is getting pretty hyped but I'd liked to mention one thing. Not to be a party pooper but most random events should be discreet and not last long. If they happened all around the lobby or tower I don't think they'd be as cool not to mention that constant giant random events causing cosmetic changes to the entire map could get rather irritating after a while.
Things like having random objects washing up at the shore, UFO beach crash, finding one unit and having TVs idly display weird ads are perfect. Of course we could have the occasional gluttonous rain, earthquakes and giant tsunamis but I think if these occurred often it could get pretty annoying.