People confuse wax and polish to be one and the same thing but actually, they are quite different. Wax is a non-abrasive coating which shields the paint and fills in the small dents and dimples to make the car shine. While the polish is a mildly abrasive product that tends to even the surface of the paint and allows it to glisten.
Applying wax over a poor painting job will seal the imperfections and will in no way improve the look of the car. On the other hand, polishing is done only when the paint is flattened because paint finish degrades over time because of the dirt grime and road film. Every time polish is applied, it removes a small layer of paint thus doing it too often can damage the paint and the only to fix it would be to spray it.
The first thing that needs to be analyzed is the location of the paint defect, whether it is under the paint or over it. Wash the car and feel the paint with your fingers, if it feels rough or slightly sticky then the imperfections are above the surface. If it feels smooth then the problems are below the surface. The defects which are present below the surface are much likely to be fixed through polishing while the defects above the surface are best repaired by a clay bar.
Take a close look after the clay bar treatment; if you still spot problems then they need to be polished out. If you find any scratches and stone chips, they need to be touched up before the application of wax.
Polishing the car
Start off by applying cutting paste to a cloth and begin to rub in a circular fashion; try to use a lot of polish and do not let the cloth dry out. In order to remove a scratch or flaw, try to fade the fresh paint to the old paint to ensure that they match. An electric polisher can make the job a lot easier but it can cause too much removal of paint thus exposing the undercoat; so be careful or just avoid it. Applying wax with electric polisher is helpful and provides an excellent finish.
Many abrasions from keys, scrapes in car parks and other nicks can be almost entirely removed with polishing. A nasty scrape is rendered virtually invisible with a bit of polishing. So, before you take the car to a body shop for a spray coat have a go at polishing out the damage and see what the true extent of the damage is.