I would only attempt to put a visible dot on the new moon, or the unlit site of a partial moon. Overwhelming the bright side of the moon to a point where you get visible contrast with the sun-lit part of the moon is another challenge entirely.
Obviously the light source would not have to be as powerful as the sun, as long as its directional like a laser. The sun puts out an equal amount of light in all directions, and the moon only captures a minute amount of that. That said, this irradiation is comparable to that on earth, in the order of 1 kW/m2. If you wanted to light up a speck of the moon, say a 1x1 km area, as brightly as the sun does, that would require a gigawatt of light.
If the smallest detail in the moon you can see without a telescope is a bit bigger then that, say 10x10km, that goes up to whopping 100 GW.
Hitting a spot that small would also require a laser with very good divergence - a good 'normal' laser with a divergence of 1 mrad would light up an area 400 km in diameter on the surface of the moon, and even with a good beam expander that figure doesnt drop under 40x40km.
Roughly adding those results, it would take the output of the entire US grid to power a laser (given its pretty efficient too) to light up a visible dot on the bright side of the moon, and this only works when its optimally focussed. Its something we could do if humanities future depended on it, but otherwise its not remotely feasible.