I've read in a few places about how in the early Church people confessed openly in church.
While one can read this in various secondary sources, I think it is a bit misleading. Early Christians weren't doing a public version of what we now call "confession," i.e. they weren't lining up every Saturday or Sunday to tell the whole congregation how they got mad at their kids, lusted after their slave, and neglected their prayer rule.
Rather, it was understood that committing certain sins totally disqualified you as a Christian -- specifically apostasy, murder, or adultery (all three of which are condemned by St. Paul as sins that bar one from the Kingdom). If you committed one of these, you were cast out of the Kingdom, having made a mockery of your Baptism. Thus, you had to re-enter the Church as a penitent. And that was a very public thing. You would have to spend X amount of years standing outside of the church doors, confessing your sin, asking for forgiveness from the true faithful who were entering for the divine services, etc. There was a whole process for this type of public confession and penance.
For example, Canon 87 of Trullo, decrees: "But he who leaves the wife lawfully given him, and shall take another is guilty of adultery by the sentence of the Lord. And it has been decreed by our Fathers that they who are such must be "weepers" for a year, "hearers" for two years, "prostrators" for three years, and in the seventh year to stand with the faithful and thus be counted worthy of the Oblation if with tears they do penance."