Tim ... well ... just be careful what kind of chemicals are used.
Those aluminum tubs really reacted to the chemicals in detergents and bleach; that definitely darkens/discolors them.
I have found that the only detergent that I like to use is original Tide. It doesn't have the oxygen bleach in it. The original Tide tends to "draw" some of the shine back to it. I don't use chlorine bleach when using Tide, however, that darkens it with one wash and I have to do a plain wash with hot, hot water and lots of plain Tide to get it back. You can even smell when the aluminum is oxydizing; that can't be healthy, huh?
If the tub is really discolored/oxydized, the only way to bring back part of the shine is to sand it with very fine sand paper then use "Mother's Cream" to restore some of the shine. Mother's Cream works really well when the aluminum becomes exposed. Use lots of clean terry-cloth rags; you'll get better results and make sure you're in a vented area. I've also found that a palm sander works better and saves your wrist. The crown is the easiest; the tub is quite difficult to restore. If you get the crown all polished, it makes the whole thing look better.
Make sure that you always thoroughly rinse the tub, lid and crown with warm water after each use and dry it completely. Once you have exposed the aluminum with sanding and polishing, it tends to discolor quicker and needs polishing more often. I think Maytag put some sort of thin lacquer "finish" on these tubs; I've never tried to do that, however.
Also, I have discovered that you can easily and successfully use a "soap" like finely grated Fels-Naptha with GREAT success in the Model E. You can even safely use Clorox or Hilex without discoloring. I am guessing that the soap contains a fat that puts a "film" of sorts on the tub and keeps the chlorine from discoloring the aluminum; you can even see the water beading up on the tub when you drain it. Fels and bleach is a very strong combination, however; you need to make sure you rinse, rinse, rinse.
I hope this helps; those tubs were hard to maintain. I guess most homemakers were only interested in the size, washing aspect, heat retainage, and lid on the Model E and didn't care if the tub discolored or spotted.
Geoff