Focusing on the dither itself: IMO, I think you're using it gratuitously.
As far as I could understand this technique (I'm also studying it), logic tells me that dithering would be useful and justifiable in three situations and both involve working with very limited palettes:
1. You may dither two colours together (50% - 50%, like you did on your 1st image) to create the illusion of a third colour. In your case, some colours were
created exclusively to be used in the dither, thus defeating the purpose of expanding the palette! In the beak for instance you could've simply just used a lighter solid (non-dithered) orange as shadow, since it isn't required anywhere else as a dark orange.
2. Also, when you don't have loads of colours available, you inevitably will have to put two clashing colours together and make transitions between them look as smooth as you can.
Arachne's work is definitely a good reference on this subject. Make sure you check it out!
3. You may also mix both of them! But it's hard as hell.

Check out the image bellow. It uses a Amstad CPC 16 colours palette, wich is pretty small for 160 x 200. It exemplifies all dithering features and looks pretty good.
(Image by Tocky)Finally, it's needless to say that some artist
have the ability adapt these "rules" and produce the most beautiful pieces (and that's the whole point, isn't it?).
So start studying them, but never be afraid to do lots of experimenting on your own.