Okay brace yourself for some harsh critique. I'm not a master myself so some of this might be nonsense, but you should see for yourself.
I'd try this:
Add some shading... Make one arm darker and dither the torso.
His arms look great when he's walking down, but seem to hardly move in the other direction.
Due to the way his head tilts forward while moving up, it looks like he's moving backwards. The torso should be in front of the head, not the other way round.
Use colors (one pixel or something) to show which arm is behind, which one is in the front.
It's interesting to see a nose with this character size. It makes the hero look young and droll I think, but that's just my feel.
I agree on the hair being a problem, especially when facing up: The shading makes it look kinda wormlike, especially the strand on the top left. In fact, the thing to his right ear shouldn't be divided from the rest of his hair when looking up. The reason it is divided when he's looking down is because hair != face.
I don't see a pattern behind the shading in the hair. I think there should always be some reason to have a shade, like distance, light, or just manipulating an area into one direction or another.
You could try and make the hair move while walking, too.
I'm not sure if I agree with that missing black pixel in the right-foot-forward-going-down frame.
Have you looked at an animated version? The walking animation might look strange due to the fact that the feet are basically a box with a diagonal in it which is jumping from side to side.
As for the facing left and -right versions, I suggest playing with outlines between hair and face. No idea what might happen then.
I recommend looking in detail at these walking frames, too. They seem jumpy. Also: left arm right foot, right arm left foot!
Then you'll notice the reason you put his head one pixel down in the walk-forward frames is because he's actually tilting towards the camera, not because he suddenly became smaller.
So in your walking frames, you should make him more diagonal and make his head stick forward, not down!
PS of some sort: Read the tutorial again and try to remake some of the other examples he shows (like the FF characters), outline by outline, flat color by flat color, shading by shading. Whenever you add a pixel or don't add a pixel, think about why the artist added that pixel or left it out.
Then when you work on your own art, think about every pixel you add or remove. Because in 16x24 (?), every. pixel. counts. ;)
Okay, critique over.
Kind regards, Jonas
PPS: I recognized the hair and was giggling a bit because I read the tutorial myself two days ago. It really helped me get my first pixels on the screen :)
