I've always thought James 5:16-Therefore confess your sins to each other and pray for each other sounded like we needed to be specific but I don't see that happening very much but don't know if it means before the assembly either.

The letters of the New Testament do not directly say much about Christians confessing sins to another person. James specifically endorses doing so in 5;16, and John speaks of confessing our sins to receive forgiveness, though he does not specify confessing to a human being rather than privately confessing to God (1 John 1:9).

Jesus commanded his disciples to be reconciled to those who had something against them (Matt. 5:23-26) which would often require confession of wrong doing and restitution (consider Zacchaeus, Luke 19:1-10 and the prodigal son, Luke 15:17-24). This was consistent with the teaching of the Law (Numbers 5:5-8 for example).

Private confession may be sufficient to reconcile a person to God, but when another has been wronged it may be necessary to confess to the one who was wronged in order to be reconciled to them, and allow healing for all concerned (healing is very much an aspect of James' subject). Still, in most cases such things should usually be kept at a personal level (note the restraint and progression in Matt 18:15-17) and dealt with as privately as possible, for all concerned. Rumor, gossip, and alliance-building are always destructive rather than reconciliatory.

Some kinds of sins do not allow restitution. One of the reasons sexual sins are so destructive is that there is no restitution possible (1 Cor 6:18). This is made worse by the fact that the betrayal of sexual sin (adultery for example) may be made even worse by confession to a spouse. Confession, acknowledging wrong in such a case where the sin is not publicly known, may be best made to a trusted Christian with the wisdom to provide some accountability without increasing the damage by sharing the knowledge with anyone else. The injunction to "speak the truth in love" (Eph 4:15) and "do not let any unwholesome talk come out of your mouths, but only what is helpful for building others up according to their needs" (Eph 4:29) must be considered as a restraint on blatantly telling people anything and everything in all circumstances. It would be wrong to use confession as a means of "taking a load off" one's own chest if that action puts an undeserved burden on someone else, so there are limits on what should be "confessed" to whom.

As realized by AA, any persistent sinful behavior is more likely to be overcome if there is human accountability, another person or persons who know of the weakness, share in prayer about it, and remind one of their responsibilities and assets. James says, "confess your sins to each other and pray for each other." The implication there is, I think, that we choose fellow believers who are going to be able to help and support us to confess to, not that we make wholesale confession of all our failures with regularity to the whole church.