Obviously if someone is just logging in to look at the game, absolutely no movement of units should be permitted. Would it be risky to allow reversable movies, such as changing the tech to compare beaker costs or move around citizens in a city? That would be the major gray area- if someone moves a citizen to a mine to see the effect, then forgets to move him back, that messes up the game.
Looking at the demographics, foreign advisor, etc. should be no-brainer-allowed, if we post the password.
I personally am iffy on allowing reversable moves (I don't have any concern over "sabotage" by moving things around and leaving them changed on purpose; if anything went wrong, I know it would be accidental), but would be okay with just looking around.