What I've learned with spriting in the school-of-hard-knocks sort of way that I learned, is that the less colors one uses, the better it looks in the end typically.
Generic:
Use the skin color for anything white/gold/tan-ish, the clothes typically little more than three variations of colors (with leather counting as a color if present), making sure the borders are of the same color (dark purple and light purple borders together look odd, for example). A good rule of thumb is this: if you only use a color in a single (small) place (say the leather of a belt), question if you should put it other places (would it fit on the gloves or collar, maybe the cloak), or see if you can substitute it with a color you're already using (maybe the darker skin tones would work better than the brown). These are just some examples of things I do, and there's always times when its best one should deviate.
1]: Solidifying the colors would help a lot with the mug, as well as extending the hat a touch. Maybe have it connect with the scarf, and the scarf with the shirt to make it look like a hooded tunic, or perhaps just the scarf to give it the appearance of a cloak.
2]: The colors are very garish, but otherwise I don't see much issue. Maybe have the collar white be the same color as the hair, or perhaps the green, as it stands out a touch due to its different color. Maybe darken the inner purple, or lighten the edge so it doesn't make the 'edge color' so visible. You want it to contain, but not distract.
3]: The only issue I see with this one is some with the scarf and the cloak, as I see some grey in between them, and some grey on the top of the scarf. The hair is a touch oddly colored with the bright purple in there. Maybe have it fade into the hair a bit more by darkening the blue or lightening the purple?
4]: Only issue I see with this is that the hair is cut off a few places with a few pieces that should be similarly cut, and some strey greens in the armor and feather.
5]: Looks good to me, I see no issue. Purple is used on a large object, silvers used in several places, outlines look to match, and no stray bits.