Should it be acceptable for a preacher to reprimand an individual in front of the church?

Answer:

"Now when Peter had come to Antioch, I withstood him to his face, because he was to be blamed; for before certain men came from James, he would eat with the Gentiles; but when they came, he withdrew and separated himself, fearing those who were of the circumcision. And the rest of the Jews also played the hypocrite with him, so that even Barnabas was carried away with their hypocrisy. But when I saw that they were not straightforward about the truth of the gospel, I said to Peter before them all, "If you, being a Jew, live in the manner of Gentiles and not as the Jews, why do you compel Gentiles to live as Jews?"" (Galatians 2:11-14).

There are times when a public rebuke is the most effective way to get someone to see the error of their way.

"Do not receive an accusation against an elder except from two or three witnesses. Those who are sinning rebuke in the presence of all, that the rest also may fear" (I Timothy 5:19-20).

When a person sins in such a way as to lead multiple people into following after his sin, then it is best to address the issue where those following after can hear why the person is in the wrong.

One last example is Ananias and his wife who lied before the church and was likewise rebuked before the church:

"And he kept back part of the proceeds, his wife also being aware of it, and brought a certain part and laid it at the apostles' feet. But Peter said, "Ananias, why has Satan filled your heart to lie to the Holy Spirit and keep back part of the price of the land for yourself? While it remained, was it not your own? And after it was sold, was it not in your own control? Why have you conceived this thing in your heart? You have not lied to men but to God." Then Ananias, hearing these words, fell down and breathed his last. So great fear came upon all those who heard these things" (Acts 5:2-5).

These examples are not to imply that every problem is handled by public rebuke, but it is certainly clear that public rebuke is neither wrong or uncalled for in all cases.