How to you make old screening in screen windows and doors look good again?
Soap and water doesn't work.
You can make the old screening on your windows and doors look good again by using a mixture of vinegar and water solution. You can also use Ammonia-free Windex Glass and Surface Cleaner or Sparkle Glass Cleaner to clean the screens. Read more on http://www.ehow.com/how_6733714_clean-screens-screen-doors-windows.html.
The aluminum has oxidized... there really isn't much you can do other than try a product specifically designed to remove oxidation from aluminum. You might try wheel cleaner for aluminum rims if you can't find anything else.
Vinegar & water works sometimes. Use newspaper instead of paper towels. If the look is still dingy, it's just old, then get a gray colored paint spray at a hobby shop.
If you are the least bit handy around the house, then screens are very easy to replace with new fiberglass screening.
brush them lightly. make them tight again with that screen tool.