I've already dealt with the basics of how redstone works, but still some oddities can arise.
Let's take a simple system:
Except here's the catch - remove the bottom connecting 'legs' of the wire, but not the ones either side of the torch, and the bottom pistons still fire. Except there's no power running to them. Cut off only the upper wires and results are as expected - only the bottom piston fires. Cut off both sets of legs and no pistons fire.
It gets worse. With power flowing disconnect both pairs of legs. Then reconnect only the upper pair. Despite this being the same configuration as first described only the upper and middle pistons will fire. It requires either the reconnection of the bottom legs or the power to be toggled to fire them all.
There's more fun to be had:
Two more images: