Actually, there were two different costume puppets used for Pufnstuf.
One was operated like you were mentioning with his arms and hands clearly moving, while his head and mouth do too; I believe this is achieved by the puppeteer giving a bit of a bounce to the head so the mouth will open and close (haven't you ever notice it seems like Puf bobs his head when he talks sometimes).
The other had the arms completely stuffed, so they just basically hang there motionless, the head seemed to be operated almost like an actual puppet head, with more adequate lip-syncing; the puppet also had the eyes that could actually spin around in little circles, which was probably achieved with some kind of mechanism built into the head.
You can tell the difference between these two puppets, the first I mentioned has a smaller, triangular shaped head with shorter hair and a notch in its upper lip, while the second of the two has a large, rounder head with more brighter hair, and straight lips. The second has a rosier mouth inside as well, while the first's is a paler pink.
Just my thoughts.