Dawn is great stuff. i have long used it on my small farm to wash animal equipment, and last summer our vet recommended it to clean out an abscess in our pony's ear.
I also use it with vinegar to keep the shower clean. Starting with a clean shower, I spray the shower, walls and tub, an hour or two before I shower, then squeegee the walls when I'm done (I wipe the corners and chrome with a clean cloth). I have never had to do any additional cleaning and it all looks brand new. It is soooooo worth the few minutes it takes. I mix about 10/1 vinegar to Dawn.
I started the when the shower was new, if you've used an abrasive to clean yours, and the surface is compromised, it might now look as nice.