Just an observation, I clean the top and windows first, then the hood, then the trunk, quarters and doors. I do the front bumper, and rear bumper last. I wash/polish the exhaust tips before I even do the wheels because it takes more time.
General rule of thumb is to wash from the top down, which is why I don't worry if I'm doing the doors/quarters in any particular order.
Where I differ is in the order of washing. I do one panel at a time, and I rinse each panel as I wash.
I leave the rear bumper for absolute last because of the contaminates it picks up from the slip stream.
I leave the front bumper for second to last because of bugs etc. Bug pieces can scratch the paint, and they're hard to get out if the fine particles of a wash mitt.
Also, I use one bucket of water/car shampoo, and the other bucket CLEAR water. No soap etc. this makes it easier to check that everything lifted from the paint has been rinsed from the mitt/sponge etc.
Just my opinions

Edit: I know this is an old thread, I don't care
