Not if we use regular laser pointers.
The first thing to consider is that not everyone can see the Moon at once. We could gather everyone in one spot, but we learned our lesson about that a few weeks ago. Instead, let’s just pick a time when the Moon is visible to as many people as possible. Since about 75% of the world’s population lives between 0°E and 120°E, we should try this while the Moon is somewhere over the Arabian Sea.
We can try to illuminate either a new moon or a full moon. The new moon is darker, making it easier to see our lasers. But the new moon is a trickier target, because it’s mostly visible during the day—washing out the effect.
Brightness aside, an ideal time would probably be 2:00 PM EST on December 27th, 2012, when a full moon will be high in the sky above Mumbai and Islamabad. At that point, the Moon will be visible to approximately five billion people—most of Asia, Europe, and Africa—about as many as can ever see it at one time.
But let’s pick a quarter moon instead, so we can see the effect on the dark side. We’ll avoid the December 21st quarter moon to avoid encouraging any Mayan nonsense, and pick the one on January 4th, 2013, half an hour after midnight (GMT). It’ll be day in East Asia but night in Africa and Europe.
Here’s our target:
The typical red laser pointer is about 5 milliwatts, and a good one has a tight enough beam to actually hit the Moon—though it’d be spread out over a large fraction of the surface when it got there. The atmosphere would distort the beam a bit, and absorb some of it, but most of the light would make it.