At this point you can effectively bring up problem areas with each side’s positions by asking neutral but realistic questions. For example, if one person says that she loves to play Beethoven really loudly in her apartment because it is wonderful music that everyone should enjoy, and it really helps to calm her down, ask her how she would feel and react if her neighbor felt the same way, but instead played Bon Jovi? Or ask if she would be able to calm down just as successfully if she listened to her music with earphones. Questions like that are neutral, but bring up realistic problems and possible resolutions.
Once the discussions begin, never use dismissive or disparaging words about any of the participants or their positions, and do not allow anyone else to do so either. Some examples of these are: “Oh, I will just pay ‘nuisance value’ to settle the case,” or one person saying that someone on the other side is a fraud or a thief, or even calls the other party a “jerk,” “dirtbag” or “slimeball,” etc. If that happens, immediately interrupt and say that such words are counterproductive, off limits and not allowed. And be firm about it, because almost nothing will poison a settlement discussion like comments of this kind.