Wow, those are some serious buffer marks! Certainly don't bring it back to the dealer. If they didn't do it right the first time, what makes you think they will do it right the next time? Every time they take a machine to your car's paint they are removing some of the clear coat and there's only so much they can remove before it's all gone (and there isn't all that much to begin with). This is borderline vandalism, in my opinion, as these people are negligently damaging your property.
I've become a bit of an expert on black Nissan / Infiniti paint this year as I've fixed a few cars that looked just like that after someone inexperienced hacked it up. Their formula for "buff and wax" might work on most cars that come through their shops, but it certainly does not work on black Nissan paint. See this thread:
http://www.autogeekonline.net/forum/show-n-shine/94011-saved-2011-infiniti-g37xs.html
Your first step is to determine if you have "scratch shield paint" which is a proprietary paint system offered by Nissan. Lift up the hood and look on the underside towards the cowl, you should see a sticker that designates this special paint.
If you do have this paint, and I suspect you do, have no fear because you can easily tackle this project yourself. The Porter Cable should do the trick no problem. When you order, ask that Autogeek substitutes in 5" pads and the proper backing plate. I would recommend the green Buff and Shine pads (
Buff and Shine Green Foam Polishing Pad - 5.5 Inch). They have enough cut to get out the damage and they are soft enough that they won't mar the paint. I would also recommend HD Speed (
3D HD Speed). It's an all in one cleaner / polish / sealant. You won't need any special wax after you use this product, it protect the paint as it polishes. Lastly, invest in good high quality microfiber towels and treat them right.
There are videos readily available about proper use of the Porter Cable, give them a watch. I would imagine you can do this job yourself for somewhere in the neighborhood of 200 bucks and an afternoon of your time.