When building such an animation, on each new frame I start by placing what's supposed to be in the same position as in the previous frame : Very often, it's a foot in contact with floor. The exact pixels may move a little if there's some shuffling or spinning, but typically a character spins on the ball of his feet, and this specific part needs to stays anchored in place.
Then I'd check the heavy or important body parts:
- shoulders (or more specifically, the logical point which is midway between the shoulders)
- head - it is heavily constrained by the shoulder spot, but neck allow quite a lot of rotation, and viewer focuses often on faces/heads.
I tend to disregard knees and elbows, because they can be deduced from the others.
Over the course of animation, check that each of these points has a logical and consistent movement. Even if you're comparing very few frames, or very different ones, you still had better harmonize them (limb proportions, volumes, and even general color/lightness).
If you have a cycling animation, check that the "trajectory" of these elements is smooth... circle, ellipse, egg-shaped. if a body part has a star-shaped movement, it means the animation is jerky and probably not following a natural path.
You can see the same principles are used in the (good) animated smileys