1. What he refers to as "moderator rods" are actually control rods. The term "moderator" refers to a material that is unlikely to absorb neutrons, but likely to scatter them. This helps lower the average neutron speed inside the reactor, which actually increases the fission rate. Since water serves this purpose just fine, most reactors do not have specific "moderator rods", although BWRs actually run pipes of liquid water through the fuel assemblies for additional moderation.
2. BWRs are not run all-rods-out, like he claims. BWRs are generally run with significant control rod insertion, so that the water stays liquid for a greater portion of the height of the core.
3. He doesn't quite explain that the source of the hydrogen is a replacement reaction where zirconium and water react to create zirconium oxide and hydrogen gas.
4. Xenon-135 is a fission product, not produced by neutron activation, and neutron activation of coolant is nothing to sneer at (the half-life of tritium is 12.3 years).