Only Jesus is infallible, no other human, not Benedict, and not FYM or EGM. So they can make errors, just like I and you can make errors. Parts of the Bible can be hard to understand. But when Jesus comes back, he will explain the difficult parts to us (1 Cor. 13:10).
I agree with you that God does not have blood, but Acts 20:28 can be translated "church of God which he acquired with the blood of his own". I think that is a better translation, since the Greek does not say dia tou haimatos autou ("with his blood"), but instead dia tou haimatos tou idiou ("with the blood of his own"). And God's own is Jesus.