Enemies of the Lord use this occasion against us to this day. It is presented by them that Israel was apostate and rejected of God long before this event and that God's effort had long since been with them and their religion. This would mean too that the blood line to the Messiah was no longer through David which would eliminate the rightful claims of Christianity.
There seems to be an observable transformation in Peter having the Spirit now. We have not heard Him quote and reason Old Testament scripture before let alone so boldly with such confidence. Just days ago he was part of a group that was over extending itself beyond the direction of the Spirit, but now he seems fully in step and infused by It. The Spirit is bringing Jesus' words and teachings to effect and Peter and the group are an observable example.
The spectacle of the manifestation of the Spirit is providing the opportunity, the revelations (past/present/future) by the Spirit is providing the conviction, the unity in the Spirit is providing the furtherance and continuance. The very presence of the Spirit in this manner is the absolute proof.
Peter received correction. Had he been the first Pope and had the Pope been given immutable divine interpretation as supposed by Roman Catholic doctrine, he would not have needed correction. Paul would have shamefully exceeded his lesser authority. Their doctrine follows from a possible misinterpretation on the proclamation Jesus made that on 'this Rock' He would build His church. Rock more likely meaning the divinely revealed faith and not just Cephas 'the rock' personally kjv@Matthew:16:17-20 (literally - You are 'piece of rock' and upon this 'massive Rock' (which flesh and blood have not revealed) I build my church).
tsk@Lamentations:2:14 Here are numerous reminders that the Lord had exposed the false prophets to them on several occasions and yet they still listened to the others. False prophets did not end during this captivity nor did they end in the time of the early church. They remain and flourish today. They are exposed over and over and yet do we listen to them. It is in part because the true prophet discovers our inequity, in part because we are self justified and vain, in part because our image of God does not allow for Him to do this.