The moon moves across the sky with an angular motion of about 14.5 degrees each hour, and the moon has an average diameter of 31.7 arcminutes. So it moves about 27.5 lunar diameters each hour, 0.45 diameters per minute or 0.0076 diameters each second. They say the moon's diameter is about 3476 kilometers, so that's about 26.4 kilometers (0.0076 * 3476) of lunar surface moving past each second from a fixed spot viewed from earth.
Light from the moon's surface takes ~1.3 seconds to reach earth, so any given spot a telescope is aimed at is actually behind the true position by about 34.32 kilometers (1.3 * 26.4) due to lightspeed delay. If a laser is aimed there, it will also take ~1.3 seconds to reach the moon's surface and miss the spot it was aimed at by double that amount - 68.64 kilometers.
Note that not one single description of the LLR experiments mentions taking this distance offset into account.But lets go ahead and pretend they do and the laser is aimed ahead with the appropriate offset.There is still a problem. A BIG and insurmountable problem!The retro-reflector cannot aim light back towards earth at an offset - it can only reflect back at the exact angle the light was received, so the reflection will be aiming exactly at the
apparent position of the light source at the moment it is received - and by that time the apparent position will be 34.32 km off from the true position on earth's surface, and the light will therefore be 68.64 km off from that position when it is reflected back to the earth.
It is claimed the reflected beam has a diameter of 20 km (an absurdly low divergence, but let's pretend it's true) when it reaches earth (see
http://www.lpi.usra.edu/lunar/missions/apollo/apollo_15/experiments/lrr/ ) - but it would hit a spot on earth's surface nearly 70km away from the observatory, which means
no portion of it's 20 km beam diameter area would come anywhere near the observatory's telescope!Get it? The whole damn thing is impossible and it's proven so with their own numbers.