As the boys above said, Clay bar to remove embedded stuff if the surface feels rough after washing. You can test this by lightly dragging a cotton cloth across the surface and noticing if it drags or leaves little cotton balls behind, if it does the clay bar is the trick.
It doesn't sound like the finish is in real bad shape but rather has some very fine scratches that need addressing. This can be done with many manufacturers products but the all have various steps/tools/compounds that must be used/followed. Like Randy said, Meguiars is one of them. I use Farecla and Norton and they both have different steps depending on the condition of the finish, depth of scratch etc. believe it or not, search YouTube for demo video's from some of the aforementioned manufacturers, they all have them out there with comprehensive mini lessons on use of the product.
My wifes car has Chryslers newer PRX brilliant black metallic pearlcoat that looks like crap if not maintained. I am very fussy about washing and maintaining the finish on the car and just like you describe is subject to very fine 'washing' scratches that are noticable when dusk settles in. In between the major rub it gets once a year I use a 'detailer' to hide the micro fine scratches. I have been using Eagle Ones Nano wax spray, its a clear product that literaly wipes on, wipes off with a little elbow grease and takes the eye away from the minor imperfections and helps give the car a wet look. I use this every 2 months and works good. Products like this are used all the time by the show car guys as they don't leave white wax behind.
If that doesn't work, likely a power polish with a super fine cutting polish and a good hand rub. BTW, the best polishing cloth's today are the new Micro Fibre type. Just bought a big package of them from Costco for cheap. They feel rough but leave the nicest shine...