How to remove  soap scum found in the bathtub and bathroom mirror? 

An ounce of prevention is worth a pound of cure when dealing with soap scum. Switching to liquid shower gel from bar soap will eliminate the talc in soap that tends to collect, along with body oils, on mineral deposits left behind when water dries on shower walls. Thus, wiping after each use with chamois or squeegee tends to minimize soap scum and mineral deposits. Keeping shower walls waxed to provide sheeting action is helpful. Do not wax shower floor, because it will be slippery and dangerous. Wiping down tile shower enclosure walls with lemon oil also retards the formation of soap scum.
There are many commercial cleaners available for shower scum. The secret is to apply and give the product time to dissolve scum. Reapplications may be necessary for severe buildup. Janitorial supply stores carry strong, alkaline degreasers for oily, soap scum removal. Automatic dishwasher detergent works well as a degreaser. Mix about ¾-cup in a bucker of water. Sponge solution on and let set 15 minutes. Keep applying to keep surfaces wet, in order to soak off scum. Scrub with a white nylon-backed scrubbie. Repeat applications may be necessary to removal all scum. Rinse and dry. Baking soda and water paste make an effective scum remover. Spraying hot white vinegar on walls is also effective on scum. For severe mineral deposits, there are products available to remove calcium, lime, or rust.  Whatever cleaner you decide to use, give the product or solution time to dissolve and degrease shower walls. Repeat applications and white scrubbie may be necessary. Daily maintenance and a weekly cleaning should minimize problems with soap scum and mineral deposits.