It works!

I said earlier that I would experiment with alternative uses for dryer sheets, among them cleaning soap scum from a shower door.  The results are in:  it works beautifully!  It took two dryer sheets to clean our shower door.  It does take a bit of elbow grease, but no more than it would take to scrub it with a bathroom cleaner and sponge.  Also, the technique only works if the door is dry; otherwise, the dryer sheets just get soggy.  Supposedly, dryer sheets also sort of coat the door's surface with something that keeps them clean a bit longer, so my next task is to see whether that one's true as well.