To answer your question more directly, it is generally an indication of an error if your hand moves away from your face on release. You didn't indicate whether you use a dynamic or a dead release, but Rick Welch's hand makes a distinctive flop when he releases rather than staying on his face. This is an indication of a relaxed hand flopping around like a dishrag, however, rather than hand movement, as can be seen by observing his forearm, which remains in place.
Anything other than Rick's hand flop is generally an indication of not relaxing the fingers and letting the string push them out of the way, a pluck, or creeping. Fortunately, the remedy for all three is the same: keep attention focused on the back muscles, as Arne mentioned. This is the same remedy whether you use a dynamic or a dead release.
Of course, if you're shooting well when your hand moves away from your face, then you might not have any of the three problems I mentioned. But then you probably wouldn't be writing this letter.