The argument about retroreflectors is right there on the page, although it's buried if you don't have the arguments raised previously in the Wikipedia article.
The main argument is that the lunar landings weren't manned for one or more of the landings. And indeed, right there on the page, it says:
> Smaller retroreflectors were also put on the Moon by the Russians; they were attached to the unmanned lunar rovers Lunokhod 1 and Lunokhod 2.
The existence of the Russian retroreflectors shows reflectors could be deployed without human intervention.
And further:
> Lick Observatory attempted to detect from Apollo 11's retroreflector while Armstrong and Aldrin were still on the Moon but did not succeed until August 1, 1969.[197] The Apollo 14 astronauts deployed a retroreflector on February 5, 1971, and McDonald Observatory detected it the same day.
The argument here is that if the retroreflectors were deployed by Apollo 11, they should have been detectable within the day, not 10 days after their supposed human caused deployment.
Again, this is just the argument presented, not an endorsement.