The "head sway" (sidewards motion of the head) is a tricky subject in animation. Simply put, we don't sway our heads in real life because the eye is usually focussed on one point.
The thing is, a head sway may add some dynamics and style to an animation. It's usually not something you want to exagerate, but it has its place.
The way you have it, it's subtle, it's a matter of opinion. You can take it out or leave it in, but it's certainly not a "flaw".
It's true that the legs and arms are rigid and need bending, but the pendulum motion is pretty good, so keep the current movement as a base.