It would be easier to tell if you posted the animation, not just the sheet

slow the animation speed down, and post gifs for all the sprites.  Heres what I can say just looking at the sprite sheets though.

For the south animation, it would look better not to insert a standing pose inbetween the contact positions.  It works, and if you have low frame restrictions it is an okay solution, but otherwise it can be done better.  Check this image of a basic 8 frame walk cycle from the book "animators survival kit" to see what I mean by the contact position

http://www.syrettdesigns.com/uploads/1/1/2/8/11288210/1232100_orig.jpg

so currently your south animation goes: standing pose, contact, standing pose, contact.  If you change those standing poses to where one leg comes slightly foreward, and one slightly back (and mirror those frame to replace the second standing pose frame) youll end up with an animation where in the limbs move through 4 unique positions rather than 3, while mantaining the same number of frames. 

Another thing that might help is showing the leg lifted up in some frames.  This makes it look less like the feet are just sliding on the floor, and more like hes actually walking.

Notice also in that link the way the head moves up and down.  This is because depending on the position of the legs the waist moves up and down, and the rest of the body above the waist moves with it.  At this resolution ussually moving the body up and down 1 pixel is sufficient.

I think theres a problem with the arms in the north facing animation.  I think when you swing our arms when walking they kind of come inward as they move forward, but move outward as they swing back.

The second version of the side view walk looks better, reference that link again if you need help with the positions.