There are three main defects that needs to be removed before it is of suitable quality, namely artefacts, high noise levels, and severe chromatic aberrations.
These defects exist even when maximal effort have been taken in the capture (Part I) and the generation (Part IIA and Part IIB) to minimise them. But now there is a high possibility - more than 90% from my experiences - to improve its quality to an acceptable level. Without the initial minimisation, the defects may be uncorrectable.
And so in Part IIC, what I do first with my HDR pictures, ex-Photomatix, is to import it, in 16 bit TIFF format, into Lightroom.
You can do all the processing that you do with imported pictures in Lightroom, but the most important in this context is Chromatic Aberration correction. This can be done elsewhere, eg Photoshop, but I find LR the most intuitive and convenient.
Sometimes the correction may still fail, but the HDR can still be saved if you can cropped away the objectional parts. But if that still won't work for you, you can of course resort to cloning and painting, as the last ditch effort.
After CA correction I will then export the TIFF to Photoshop, for which I have a noise reduction plugin, namely Noise Ninja.
And the first step is to remove artefacts using Photoshop's Filter | Noise | Despeckle. There may be other ways but I find this to be very straightforward and pretty effective. You can attenuate its effects if it makes your picture too soft using the various means in Photoshop.
Then I run Noise Ninja.
In Noise Ninja I use a relatively high value for USM, compared to that used for non HDR pictures, and with a correspondingly greater strength in the Luminance and Colour Noise reduction settings, particularly for the former. The high USM will conteract the softness created by the high Luminance noise reduction value.
These are the essential steps, and it can remove the three main defects completely.
You can off course thereafter do any or all of your standard Photoshop or LR routines, eg I sometimes, if it is artistically merited, apply further GND filtering to the pictures. These GND filters are digitally simulated and was discussed in an earlier blog entry of mine.
And this concludes the process of creating high quality HDR picutres using Photomatix, from its capture, to its initial generation, and to the essential secondary processing.
And as a final word, and a motivation, high quality HDR pictures, do sell a little better than non HDR ones, all things being equal.
So enjoy and good luck!