What was wrong with C1 Judaism? Was anything wrong? There must have been something wrong since Israel rejected her Messiah.
About what was wrong, scholars are divided. Surprise, surprise! The traditional answer (the old perspective) is Judaism was legalistic; it taught salvation by works. The modern answer ( the new perspective) is it was nationalistic; it saw salvation in Jewish ethnicity.
We should be grateful for scholarly research but never in thrall to it. The final and certain resource for a Christian is Scripture. There we find, surprise, surprise, that both legalism and nationalism blinded C1 Judaism.
John the Baptist warns the religious leaders not to trust in their ethnicity (do not say, we have Abraham as our father Matt 3;9) and Jesus tells the parable of the pharisee and taxcollector against the pharisees (who trusted in themselves that they were righteous Lk 18:9-14).
They did not grasp that 'not all Israel are of Israel'. Nor did they realise that Law was a covenant of works that condemned rather than justified.
They had a false confidence in both their lineage and their Law. Tragically, because of this, they failed to recognise their Lord.