Corrected entry: In the episode 'Blink,' the stone angels are able to move when no-one's looking at them. But there are some shots (such as when Sally leaves Wester Drumlin's) where no-one (except the audience) is facing the angels. Why aren't they moving? Even just a little movement, like breathing. They're still just stone statues.
Corrected entry: The fundemental feature of the statue monsters is that they cannot move if anyone/anything is looking at them. At the end they are tricked into looking at each other (by the Tardis dematerialising) and so are trapped forever. But they are in a basement with a light on, when the light goes off they will escape. In fact they earlier made the light blink so they could move and attack the good guys.