Well, I shot about half a box of fresh Federal .357 mags and all fired normally. I then shot some of the old (30-year old) .38 Spl reloads and about 20% failed to fire. It appears that tightening the adjusting screw was enough to ensure reliable firing of fresh factory ammo. The old .38 Spl may have deteriorated, and account for those miss-fires, though only more shooting with fresh ammo will totally convince me that my problem is solved.
The firing pin seems to move easily against spring tension in the hammer.