Puppet "Jerks" when using walk behavior...

My *guess* is there is something about the head or top of shoulders that is making the top of the puppet "stuck". The head does not move up and down as it walks. What then happens (is my guess) is the first frame the walk and the "stuck" behavior are fighting it out and the other one wins for the slightest of moments. (E.g. due to the ramp up time Smidio mentioned) Then the "stuck" behavior wins. So you get this single frame of strange jitter. The difference when walking in the other direction because perhaps the handle or whatever is causing it to be stuck is in a different place relative to the other handles, so it behaves a bit different.

So how to fix it. Well, if I am right, you would need to find and remove the "stuck" handle. E.g try deleting half of the layers on the head (like the eyes and eyebrows and mouth and nose) and see if the jitter still occurs, then delete more, until there is nothing left or the jitter stops. Then undo and put them back - basically by trial and error see if there is something you delete that makes the jitter go away. I consider it a highly scientific method of "trial and error until you get lucky!"