Acidic cleaners break down soap scum easily. My favorite is sold at Home Depot: ZEP Shower Tub and Tile cleaner. I prefer traditional castille soaps to synthetic detergent soaps (Dove, etc.) and this is what I turn to when I let soap scum get out of hand. It dissolves soap scum fast! And it's cheap.
I also use products like Simple Green or Holy Cow! Concentrated Cleaner when I can keep up with regular cleaning. They both break down soap scum nicely.
With both cleaners I use a cotton loop bartowel.
I wouldn't recommend Mr. Clean Magic Eraser because it is a microabrasive pad made of melamine foam. Here's some
information about how it
works.