There are two different products that I would highly recommend...The first would require you to go to Home Depot. In the plumbing section, where the liquid plumbers & toilet plungers are, is a product called "Eliminate". Its in a white plastic spray bottle with some pink, light blue & black lettering...Anyway, purchase yourself a bottle of this bathroom cleaner & use it accordingly. Be sure to have some adequate ventilation when using this product from either the bath exhaust fan or the window or both. You'll want to use a soft to medium bristle scrub brush & you'll see after spraying this product on each & every area that has this soap scum, that once applied & soaked in, will remove this scum with ease.
Part of the problem causing you to have this build up is not only from the soap & dirt built up, but from the calcium buildup concentrated in your water source. Through an extended period of time, you'll always have this buildup....Basically, you have hard water & might want to consider installing a water softener....This would for sure rectify your problem & definitely make that much of a difference with how clean you feel after have taken a shower.
The other product I recommend you'll have to purchase online to obtain. It's called "Restor4" www.Restor4.com...Now, this is some powerful stuff... It's about the best cleaner that I have ever used to not only remove this soap scum, but to bring out the natural beauty of fiberglass, tile, grout lines, glass surfaces, plumbing fixtures & granite...DO NOT use this product on any natural marble surfaces...For this will etch your marble as if it were honed.
Anyway, try anyone of these methods & you'll be amazed on how well of a job you'll end up with....Just a note & not to dis the first answer you received, but using metal tools on many brands of tiles creates these black/grey scuffs that are many times very difficult to remove.......Other than that, I wish you the best of luck & remember to were some rubber gloves...Take care....