There is already randomness. Rubber and Rockets.
Also, on Extra - Pendulum, something strange can happen. Set it up like the current best, move it slightly, then undo. The cloth at the bottom may break in a slightly different way (I've seen three different).
Rockets - See Chaos Generator. Watching the various different solutions, the rockets move in different ways - ways you could never guess.
Rubber - Any level with long strings of rubber is really annoying, as things that shouldn't be influenced are. Try tweaking Mushroom to Move, or Casius - Pistons. Weird things happen. Also see Incredible Machines 7 - Crash Test. That one was really fun, I've got probably 40+ solutions to that. You can do something crazily insane (smallest bit of rope and it'll work.) Note how on my 356 solution to Mushroom to Move I hung a little rope from an anchor point to help the armadillo over it.
Attachments are my favourite two solutions from Crash Test that I created. Could physics have guessed either would happen?
![Razz :P](./images/smilies/icon_razz.gif)