I finally got around to watching and finishing this show. In general, I thought it was incredible. I didn't love the way the show, at times, seemed to present the Church as being consumed by corruption and lack of principle, but I loved the Pope Pius XIII character (I would also love to have a Pope just like this). The acting, writing, music, cinematography - everything - was great.
This scene in particular struck an emotional chord with me. I love the way he wanders into the cabin of the airplane when everyone is asleep. This scene followed by the shot of him praying in the gas station parking lot was really beautiful and moving.
Edit: Following up on my first point, I think the corruption within the Church portrayed in the series demonstrates that the Pope/clergy is not the Church; God is. I'm not sure if this was intentional but that's one way of thinking about it.