Would there be a big advantage putting a SETI listening post on the far side of the moon?

I assume the moon would act as a large shield to diminish the radio “noise” from Earth. Obviously there would be an issue getting any information back home for the same reason.

Definitely. I once spoke to an astronomer about this. It would be a huge advantage for us to have that. The problem is building it. Just imagine. The moon is a long way away and it’s a vacuum. All that heavy equipment would have to be transported in hundreds of trips and dropped off, then assembled by … whom? Robots? People? It would be great to have it but unlikely to be built.