The lady I talked to at Weber was nice and she sent me this summary as to how we Weber owners are supposed to clean our stains and surface rust:
What you SHOULD Do
Clean the outside of your grill weekly using warm soapy water, followed by a rinse, and thorough drying
Once clean use a high-quality stainless steelcleaner and polish
Examples: Weber Stainless Steel Polish, Dymon Stainless Steel Cleaner, Zep Stainless Steel Cleaner & Polish
Apply the polish with a microfiber cloth or low-lint paper towel with the grain of the stainless steel to avoid surface scratches
A Weber grill cover is recommended to further protect the grill from the elements
What You SHOULD NOT Do
DO NOT USE scouring pads or other abrasive materials as they may cause scratches
DO NOT USE any cleaning agents containing chlorine which can be corrosive to stainless steel
Examples: Clorox, Lysol, 409 multi-surface cleaners
Removal of Surface Rust Stains from Stainless Steel Surfaces
In certain corrosive environments stainless-steel may develop surface staining when regular care and maintenance is not properly followed. If this occurs the following methods are recommended to effectively restore the surface to its original condition.
First, follow the regular care and maintenance steps (see prior section)
If stubborn staining persist, use a microfiber cloth to apply Bar Keeper's Friend, Brillo Cameo or comparable product prior to polishing the stainless steel
Remember to always clean with the grain of the stainless steel