While waiting on the mountainside, Trip goes to activate the communications channel. When he leans on the very large boulder the communications panel is resting on, it moves visibly giving away its lack of mass as it was presumably created from spray foam.
When Trip is repairing his transceiver, there is a shot of the glass dome of his shuttle reflecting a light source. Since the sun has not yet come up at that stage, it must be the reflection of a lighting equipment.
While CDR Tucker didn't want to transport back to Enterprise alone, they could have transported water and survival gear down to them.
T'Pol uses Fahrenheit rather than Celsius to describe the surface of the moon.