I had the same problem with my new mazda3. Pissed me off to no end, but I should have known better. I won't ever use a self serve coin wash again. (I can never get my car clean enough using one of those anyway, hand washing will get it
very clean)
Since I got so pissed about it, I broke the bank and got a
Zaino Bros Total Protection Show Car Kit. It kicks ass so far. It has pretty much everything you need to keep the exterior of your car cleaned and polished. The only other stuff you'll need are a wash bucket, a bottle of Dawn liquid detergent, and a bunch of good, clean, white bath towels with the embroidery cut off. I did a complete job when I first got the kit (wash / claybar / wash again / polish), and today I just washed it once and added a couple more coats of the polish to touch it up. The paint is so glossy and smooth when I'm done that if I were to set a ceramic mug full of coffee on top of the car it would slide off and hit the ground.
The kit includes Z-5 polish which will help minimize fine scratches and swirl marks. If you have some deep scratches that go completely through the clearcoat, you'll probably need something else to conceal the scratch, don't have any advice for you there yet.
Good luck.