One big assumption stuck in the middle that undermines his entire calculation:
The field of view of the receiver is larger than the divergence of the transmit beam so that it can collect light from the whole illuminated area.
That's almost certainly true over the distances involved in the other laser ranging applications he lists, since they involve aircraft or satellites in orbit. Over lunar distances, however, that doesn't hold, because the transmitted beam is a lot wider than the receiver telescope back on Earth by the time it hits the lunar surface. He is essentially saying the number of photons returned by the relatively small retroreflectors is about the same as the number of photons returned from the bare lunar surface
over the entire area of illumination. That actually pretty much confirms they are there!
In typical HB style he's done some maths based on a faulty premise. All he has done is ignore vast amounts of empirical data (his selected ranging stations will have had a lot of data available about the returned signal from the bare surface as well but he didn't bother to check) in order to show that reality doesn't match his expectations, then concluded, in typical HB style, that reality is at fault rather than re-examining his conclusion. The fact it took me all of a minute to find that single statement that undermines his whole argument, without even needing to go into the mathematics at all, shows a lot about his scientific rigour.
As, incidentally, does the fact it is self-published online with no peer review...
