I am presently engaged in correcting this problem on my 2011 R/T Blackberry. About 2/3 of the way there after approx. 20 man hours. I'll tell you up front, this will be a lot of work to do yourself, and very expensive to pay someone else to do properly. But before I finished up the upper sides today, I was starting to feel like selling the ride at some point; the swirls were just so depressing to see all the time. They made the so-dark-it's-nearly-black metallic cobalt blue look like a boring dark minivan color. Now that it's polished, it looks like a black car with neon-blue trim on the sheen lines.
Corrective steps:
0) Learn to wash and care for the car such that damage is limited going forward
1) Wash with a stripping soap (I use Dawn prior to polishing since it pretty much obliterates any wax remaining)
2) Clay to "scrub" the paint clean of surface junk. Clay is abrasive and will mar the paint, but is much more focused at cleaning the surface of debris than a rag
3) Do the plastic bag test to make sure the claying has sufficiently cleaned the surface (thin sandwich bags work well)
4) Polish with a good polish, pad, and polisher (Meguiar's 105 to start with on bad swirls, and a hearty endorsement of the Porter Cable 7424). I like the Hex-logic pads since they seem to clean up well.
5) Finish polish (Meguiar's 205 for me) to obtain your desired level of sheen
6) Wax/glaze/whatever to protect the surface, since there is no physical way for a coating to do anything but obscure what is beneath it. Fillers and dyes only hide damage at best, and lock it away at worst.
Having done everything above the belt line so far on my car, I am a firm believe of the Junkman2000 way of doing things. The guy has a ton of Youtube videos that are extremely in depth, and fully explain both how and why he does things the way he does. His way made sense, so I tried it, and I have no reason to contradict him at this point.
TCB