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.
When Trip is attacked after he crashes he uses a hydrospanner as an improvised weapon. Yet both previous and subsequent episodes established that shuttlepods have several phase pistols, as well as communicators and tricorders, in the equipment locker under the seat. However Trip never makes use of them, especially the phase pistol.
T'Pol uses Fahrenheit rather than Celsius to describe the surface of the moon.