Bob,
Polarity observation is a safety, not functional issue. Keep in mind that it is unsafe to touch the black (hot) conductor while you are in contact with grounded surfaces (concrete, metal piping, frames of grounded metal appliances, etc.) It is usually relatively safe to touch the white conductor, because it is grounded at the source and thterfore there is no potential difference to push current through you.
When you turn offf a switch, it should be the hot conductor which is interrupted, thereby rendering the equipment safe to "put your fingers in". If however the polarity is reversed, the equipment will be de-energized but the neutral and not the hot will be interrupted, thereby exposing you to the hot conductor.
Also, under certain fault conditions, if a piece of equipment is wired with reverse polarity, it may suddenly start-up by itself without the switch being operated.
