Dithering Portrait

[IrresponsibleFreelancer]

  I am rather new to the idea of dithering and i figured there was no better way to get better than to try practicing it.  I did a front view portrait of a man's face with an attempt at the strategy of dithering.  I would like some advice not only on my dithering techniques but on any other problems spotted with the art piece.  Thanks in advance. 
1st:



UPDATE: Thanks for the crit Joe.  I see what you mean with the why i would want to practice and learn dithering even without the technological limitations, the reason is because i like the looks of pixels and it also reminds me of an older game i played where its a hybrid of both dithering and modern colours.  The banding issues i tried to resolve (those that i could see) but my eye is clearly not trained enough to spot many of them.  The thread that you showed me to was very helpful in learning what banding was and how to solve it but i would greatly appreciate an edit to see what i am truly doing wrong.  Finally with the anatomy i moved the eyes of the character down only 1 pixel (sorry ) but i only did one because i wanted to maintain my style as well as the character. 
2nd:

[Joe]

As modern screens are crisp, these days a good question to ask of dithering is why.

Dithering is used either for adding texture, or for adding colors in a limited palette.
So a specific critique to workyour piece would be: you are using dithering where you already have a color that could work there. This creates an inconsistent feel where, in other areas, you are using that color.
In this piece I could see it being used for texture; maybe he has a rough stubble.
If you want to practice dither specifically, you'll have to limit your colors so that it becomes useful.
Check your banding. There are many instances of it here, get into the habit of not even putting it there in the first place (checking as you go).
The anatomy is pretty good, eyes could be 5px lower. Your contrast can safely be improved.

I can do an edit if you'd like.