I do understand that most these characters are desaturated, to almost being one palette ramp of hue/color.
That really isn't a problem, persay. The problem is, with so many similar colors, you'll have to rely on contrast more since you aren't using such a wide gamut of hues. Many of these loose a lot of clarity from lack of contrast. Hands get lost inside bodies, legs lost behind capes, facial features lost inside heads. I personally love what you've done with the character designs and matching color schemes, but most of the palettes suffer from a lack of contrast.
One general issue I have is with the inconsistent shading and detailing of muscles. For example, 1-5, 2-1, 3-3, and 4-2 have very soft lines and shades to define the muscle, whereas 2-4, 4-1, 5-3 and onward are much sharper. Lots of black lines also give the muscles a harsh segmented insectoid Dragon Ball Z look. No me gusta.

This one has some of the harshest details from the pieces I've seen, which is unfortunate, because it also has some of the strongest line art. The thing that really kills it for me is the amount of dark black lines within the sprite. I like the black around the perimeter of the sprite, and black lines can be an important asset to clarify overlapping limbs with palettes this specialized.
My edit for the most part just lightens up most of the internal black lines, and tweaking the contrast while trying to stay true to the original. Using contrasty shades does just as good a job as black lines do, and it doesn't make the details nearly as busy. The fingers where dissapearing in the pants, so I also upped the contrast for clarity. Also made some drastic changes to the shading of the arm, so it's readable as cybernetics. (Although I did lose the sheen. You could probably do better.)
Also, I HATE flat feet on large fighters. It looks horribly amateurish. A lot of effort goes into making a fighter sprite "pop" and convey volume, and flat feet ruin the whole effect for me. The previously posted Remy sprite is a bad example because he actually has the flattest angle to his stance in 3rd Strike. All the other Street Fighter 3 characters have a much steeper angle on their feet. If flat feet are intentional and you're going for some sort of old school look, keep the angle. Otherwise I'd highly recommend you give a slight slope to everyone's stance.

This piece suffers from the exact opposite of the first: not enough internal detail/contrast where it's needed. For the edit, I attempted to make the skin and shirt clearly distinguishable from the jacket and pants. Jacket sleeves and pants have folds that flow with the limbs. Hair, while probably not correct according to the original design, is readable and doesn't mix in with the red shoulder thing. Buckles and straps pop more, and no more flat foot.
Another inconsistency is lighting. For the most part, it seems to become from the top right, although on several characters it looks like its coming directly from the left. Putting the light source to the side effectively forces one half of the character in light, the other in shade, split down the middle. It also gives a pillow shaded effect in some areas, most noticeable on the torso and legs. The traditional top light source tends to make for a more readable character, IMO. Limbs especially seem more readable when an arm or leg is extended horizontally.
Anyway, despite all the criticism, I actually love the hell out of these. The ninja, especially, tickles my pickle.