When I take theater photos (student performances on stage), in my situation I've found having ADL on the highest setting works best. The curtains and stage floor are black. With the spotlights on, this yields extremely high contrast photos. When I first started photographing their performances, I turned the ADL off. Since I was using a very high ISO (no flash allowed), when editing the lighting/shadows, it was really difficult to end up with a decent photo. Now that I've set the ADL to its highest, I'm not left with such a huge difference between the darks and lights overall. However, in general situations where there isn't such a huge amount of contrast, it is best to either turn it off or at least lower its affect.
When photographing the moon, if it is turned on, the moon looks as if it is moving in the sky because the photo captures the moon's glow. Better to turn it off for moon shots especially if it is at night.
When photographing the moon, if it is turned on, the moon looks as if it is moving in the sky because the photo captures the moon's glow. Better to turn it off for moon shots especially if it is at night.