The science

Sweep a laser across the Moon and the spot it makes really does move faster than light. Flick the laser through a quarter turn in a tenth of a second and the spot sweeps at 15.7 radians per second × 384,400 km = 6.04 million km/s, or 20.1 times the speed of light. On the Moon itself it crosses the 3,474 km face in about 0.6 milliseconds.

But nothing travels across the Moon. Every photon flies straight from Earth at the speed of light; the spot is just where each one lands, a different photon every instant. Relativity limits the speed of causes and information, not the speed of patterns.

Observatories really do fire lasers at the Moon (lunar laser ranging, off the reflectors Apollo left behind).