I did an edit to the arms of your animation. I tried to get the shading slightly changed, so you didn't get the banding effect.
(http://i.imgur.com/OTyufRW.gif)
Edit: My program made it slightly faster than what it was before for some reason, and I don't know how to fix it :/
I think that you need to better define your forms. Boxcar was going in the right direction. Also you should avoid banding and using similar tones of same color for shading cause low contrast between them cause blur effect.
Here you can find some of the pixel art terms and tips explained. http://www.pixeljoint.com/forum/forum_posts.asp?TID=11299 (http://www.pixeljoint.com/forum/forum_posts.asp?TID=11299)
Here is quick edit, also I didn't have the time to create animation, but you can easily find some reference animation and learn form them. You can open gif files in PS, Gimp, Graphicgale, (even some websites) etc. and study every frame. :)
(http://i.imgur.com/GTf1zji.gif)
This was just my idea. :) Style is your choice, but you should definitely learn about banding and pillow shading and try to avoid it.
Your link definitely educated me on banding and color, but is there pillow shading on my character anywhere? I though I had do e a good job avoiding pillow shading.
(http://img.photobucket.com/albums/v84/aceallen/SQcqfGs.gif)
That should give you a bit of an idea of what to do about the hands and the values you should select for colors. The main difference is not that I simply lightened the colors, but I made the contrast between each value graduation on the ramp more stark, essentially making them more stark in their brightness difference.
I also showed you what I meant about leaving that lone pixel on the wrist and removed the brightest color on his shirt -- you didn't need that light because there wasn't a lot you could light on a dull green seemingly cotton shirt.
Finally, I played with his hair animation on a few frames, but one in particular where it almost flattens out to give it more of that 'bounce' you seemed to be going for.
Though, I am a little confused about the pattern on the shirt.