I spoke to a friend who runs a Green Clean company, and she said her staff do this on stubborn shower scum: Mix bicarbonate of soda with water to make a paste, then wipe off. Spray with cleaning vinegar - straight up, no water, or cheap white vinegar, straight, then rinse well, especially if there are asthmatics in the house. If it is really stubborn, use a cream cleanser like Jif.
To maintain, keep a spray bottle of 1 part vinegar, 3 parts water in the shower and spray before you shower - unless you have asthma.
Cheers, Rain, and thanks to Jo for her wisdom.