If you watch after Adam is saved from the sand-worms, his wife moves the horse in front of the mirror, then he waves his arm in front of it. If you look closely, you can see the reflection of his arm.
Adam's arm moves too fast to see a reflection. I looked over the scene, and the way his arm moves makes it look like he has a reflection. But he has none at all, and here's why: To create the no-reflection, the mirror is actually a window. The ceramic thingy that Barbara picks up and waves in front of the "mirror" doesn't match the movement of the supposed reflection, because someone else is behind the "mirror" waving a duplicate of the object. Doing the window illusion is much more timely and cost-efficient than using a real mirror and editing out Adam's arm.
You can see reflections in windows too. If you watch when adam walks in front of any regular window, you see his reflection. So how is this "window" different?