Moving the puppet while capturing the frame was something Phil Tippet used and coined as "go-motion." He had puppets on hydraulic pumps and electrical rigs that would move when a frame was being captured. If you don't have access to that kind of equipment, you'll most likely have to spend time brushing out rigs, rods, or however you're choosing to move your puppets.

You could try blurring parts of frames individually in photoshop. However, you'll have to pay just as much attention to the shape, movement, density, feathering and easing in and out of the blur as you would to trying to get smooth animation while shooting, because otherwise you might end up with jerky/strobing/boiling blurs that call attention to themselves.

A lot of animators use a plugin called ReelSmart Motion Blur that automatically adds blur to movement in video. Check out their website videos:

http://www.revisionfx.com/products/rsmb/

It wrks quite well. Be sure to use it sparingly, because it can become quite apparent and distracting if overused.