The arms still look like they're sliding as they always stay on the same line.

I've changed the arms so when they're at the end of the swings the "hands" kind of flit up. You'll notice also that I cut down on the secondary animations like the skirt flowing and the body shifting (which I realize I started that

) mostly because I was so distracted by it that I couldn't figure out what was wrong.
As rikfuzz said the head needs to be up a total of twice, when the feet are in the passing position (the planted leg is fully stretched up and the other leg is passing through the same other leg), so I went ahead and did that.
After that I found that it was odd that the was not moving down when the torso went down, which really didn't make sense, so the skirt moves down as well.
The thing that I think bothered me the most until I figured it out was that both feet were never on the ground at the same time. It's sort of a type of running when you do that.

I also messed with leg positions so that they would move a little smoother. As well, I added the front part of the foot only on the planted foot.
The head jiggling that you did I think would be fine but it's too choppy as it is. I think if you held the head down at the bottom for another frame or two it would be less choppy.
On the hair I added a little bounce. Not really sure if it looks good, but there you go.
I'm incredibly tired so if something doesn't make sense, I apologize.
