Protestant don't say that there aren't any errors in the scriptures we have today. What we say is that the scriptures as written by the original authors are inerrant and inspired by the Holy Spirit. We are aware that there are copyist errors and our commentators often point them out. For instance Matt. 23:35 that you mention.
Adam Clarke's Commentary
The national punishment of all the innocent blood which had been shed in the land, shall speedily come upon you, from the blood of Abel the just, the first prophet and preacher of righteousness, Heb_11:4; 2Pe_2:5, to the blood of Zachariah, the son of Barachiah. It is likely that our Lord refers to the murder of Zachariah, mentioned 2Ch_24:20, who said to the people, Why transgress ye the commandments of God, so that ye cannot prosper? Because ye have forsaken the Lord, he hath forsaken you. And they conspired against him and stoned him - at the commandment of the king, in the court of the house of the Lord. And when he died, he said, The Lord look upon and require it: 2Ch_24:21, 2Ch_24:22.
But it is objected, that this Zachariah was called the son of Jehoiada, and our Lord calls this one the son of Barachiah. Let it be observed,......
Clarke goes on to give a few different possible explanations such as one person being called by two names, which was common among the Jews and then we see in the NT Peter called Simon, etc.
......
That Jerome says that, in the Gospel of the Nazarenes, it was Jehoiada, instead of Barachiah.
That Jehoiada and Barachiah have the very same meaning, the praise or blessing of Jehovah.
John Gill's Commentary speaks of a few suggestions but agrees that the two names same person theory is probably the correct one seeing Jerome found Jehoiada in the Hebrew Bible of the Nazarenes.
Note:Clarke was of the Wesleyan persuasion and Gill was a Calvinist.