How Does One Assess Someone's Directing Skills From Seeing His Work?

Of course as the centre of the circle, the director is responsible for everything that you see and hear on the stage during the performance.  Some might argue that when watching a director's work, we are actually watching actors, so assessing the director becomes ridiculous.  However, sine they are the centre of the wheel, it is perhaps worth assessing all aspects of the performance and production.

Was it well planned and executed? Were the lighting cues sloppy? If there were, then this is the director's responsibility at the end o the day.  The performances of the actor are also the responsibility of the director too. Those performances are carefully prepared in rehearsal with close work between the actor and the director, delving into the script, wrenching from it the story of the play, to show to the audience.

If you wanted some areas for assessment, I believe you could look at overall polish, actors performance, concept, blocking and the overall production as a whole.