I'd skip the head bobbing.
The way the head is moving suggests that he is limping or that his left leg is longer than his right leg.
The right arm moves from side to side while his left arm also moves up and down, I can't tell with is better though.
His crotch area seems to be moving up and down.
I agree with the shading, it serves no purpose.
Otherwise, since this is a 4 frame walk, I think you're on the right way. Alot of beginners would mirror the legs two and two but you have 4 distinct leg frames which is great.
I hope you don't drop this animation and starts on something new.