Sometimes, the dithering algorithm can't achieve a good color pattern, because of Minecraft's limited color palette. This is mostly the case with skin colors, but can also happen with grayscale areas.
There are only a small subset of colors that can be used for skin:
Good colors:
Case-by-case:
Hard to get colors:
Can look bad:
As an example, here is Sora's 1x1 map art and Mapartcraft's output (with the preset given in here):
Although it looks decent, the cheeks are grayish, due to the usage of medium White Wool by the tool. To change that, however, is not an easy task, and is case by case.
The prefered method is, by trial and error, changing Brightness and Contrast. Here is an output example with 78% Brightness and 110% Contrast:
However, the background now became grayish with dithering.
If you want to get only a specific area from another picture, you will have to use an external editor. In this guide, I will use Paint.NET's Magic Wand's tool to get the background from the previous dithered version:
When the original image has gray sections, sometimes dithering adds Pink or Light Blue colors, as can be seen in this Fubuki:
To fix this, in Paint.NET, you can use the Magic Wand's tool with Flood Mode: Global, Rectangle Select with Subtract or Intersect modes, Color Picker (K) on a gray color and Paint Bucket (F):
Compare the results (this was done very quick, as some changed colors could be darker):
You may have heard somewhere that I (mms0316) have created a plugin. However, this is a .DLL that has to be placed in C:\Program Files\paint.net\Effects
and, for safety purposes, I do not feel I should be distributing binary code (and you should not be trusting binary code from others).
If you really want to delve into this, you will need to compile the plugin yourself. See: https://github.com/mms0316/Paint.NET-dithering-plugin-for-Minecraft-map-art
This plugin brings different results from MapartCraft, which may or may not be good.
Here are different results fiddling with some colors (medium White Wool, lightest White Terracotta and/or TNT):
Final note: do what satisfies you. There is no silver bullet.