This passage occurs as a New Testament Lesson in the RCL "Pentecost"/"Ordinary"/"Proper" Season, Year A, most recently September 2014.
Summary: Jesus seems to let us off the hook today, telling us we can treat sinning Christians like gentiles and tax collectors, as long as we've gone through the appeal court system. However, this is the worst news of all, because Jesus spends most of his time eating with tax collectors and even getting harassed for his association with them. In other words, Jesus doesn't give us permission to drop them, but rather instructs us to bear them, teach them and even get persecuted because we continue to care for them over and against their difficulties toward us. Yes, he does let us remove our heart strings a bit from them, but not our moral obligation. Hence why Jesus has to promise us his presence in the midst of conflict!
αδελφος (brother/sister; found throughout section) Earlier in Matthew's Gospel, he refers to his followers as his brothers and sisters (12:49). He is telling his disciples that in the church they are also brothers and sisters to one another.
εθνικος (pagan, gentile, literally "ethnic"; 18:17) Jesus suggests we treat Christians who have greatly sinned against us as gentiles. Interestingly, Jesus final words in the Gospel of Matthew instruct us to preach to the gentiles (all the nations of the world; same root word) and earlier Jesus reminds us to love our enemies, because even the gentiles to this. Jesus is not giving us permission to be rude and dismissive to our brothers and sisters in Jesus, even those whom we are angry with.
τελωνης ("tax collector"; 18:17) Jesus eats with tax collectors. He repeatedly takes heat for being seen with them. So considering someone a tax collector means something more like this: "Treat them in such a way that no one knows how much they anger and embarrass you, bearing your cross and thanking God for this opportunity to become a more patient and compassionate person."
συμφωνησωσιν ("agree" or "match", from συμφωνεω; 18:19) The actually meaning of this word is not that interesting. What is interesting is the derivation, "symphony" which means "together-sounds." Jesus says that if we make a symphony, God listens. Haha!
συνηγμενοι ("gathered"; passive perfect participle from "συναγω"; 18:20) This participle covers up a familiar word: synago, from which we get synagogue. The voice is significant here. We do not gather ourselves in the church, but rather are gathered God. Thus, we are moving from human action to God's promise. Also worth noting that Jesus promises his presence in the midst of the office of the keys and congregational conflict. The church is a gift, however human and sinful it can be!
Translation Issue: Hypothetical situations with εαν
Technically, this word is a combination of: ει αν, both of which are "subjunctive" markers. Put them together and you have a very hypothetical situation. If you have the word εαν, the writer/speaker is not specifying if this will actually happen. It means something like, "if" or perhaps "whenever." If is used in Greek to set up a simple phrase (so necessary for science), if-then. So in our text for this week, Jesus is not promising conflict; nor is he promising that people will not listen. He is simply saying, "If you experience this, well, then do this..."
Also worth noting: Every other verse in this section has an "if" clause, yet in 18:20 Jesus simply declares -- Where two or three are gathered, I am in the midst of you.