How To Be Successful In Neighborhood Dispute Mediation
A good mediator will start people talking, then, they are hoping the parties keep it going on their own, with them only jumping in if conversation gets sidetracked or unproductive.
Before even going to the mediation you need to get your game plan figured out. Look through all your documentation, and theirs, that you have. Find the untruths that you can prove, find any inconsistencies or conflicts in their story and have them listed on paper or memorized (preferably memorized). Unless they are an incredibly skilled liar you can bet there will be something you can use to throw off their game.
When conversation starts let the adversary lead a bit. Typically the lies or inconsistencies will be brought up by them, since, if it was important enough to lie about to make their story "better" it's likely something important enough for them to bring up in negotiations. Let them take it there, when it gets to the right point, use your proof or your questions of inconsistencies at that point. They will have a plan worked out as well (most likely, anyway) and if you trip them up when going a direction they are leading, it could throw them all off course.
By taking this route you will undoubtedly frustrate the hell out of them, and you will increase the likelihood of getting a hostile or uncontrollable reaction. You WANT the mediator to see this so they understand what you have been dealing with. If you know the buttons to push, push them, but let them get you within range so you don't appear to be a troublemaker.
In addition, be aware when they start throwing out baseless or unsubstantiated accusations about how fearful they are of you or accusing you of various acts harassment and be sure to ask them to get more specific. Ask for dates and specific events, rather than just sweeping accusations. What happened, what you specifically did to cause fear or intimidation. If there truly isn't any, they will stumble and stammer, if even for a few seconds before they come up with a story, it will be enough time for a skilled negotiator to read that person's apprehension.
Do not even let them get away with a general, sweeping accusation without you asking them to get specific. The more times you can get away with that, the more you prove your case. This is exactly what a good harassment attorney would do in court as well.
The Chances of Success
I have new respect for the topic of international relations, the war on terror and such topics after this process, as I understand the position diplomats are in. This is due to one simple fact that proved itself in technicolor during our mediation experience:
In order for mediation to be successful, all sides involved need to actually want to resolve the issue.
In some cases, one party may not actually want resolution as they either enjoy and want the drama to feed their own self worth by having to "protect their family" or some such thing, or it's the absolute compulsive need to be right and the complete inability to accept responsibility for their actions. Such is, I believe, our case...some folks just love to "be a victim".
Some people simply are not happy unless their mad.
If you are dealing with one of these types of people, mediation will fail, because they will want it to. You may well reach an agreement, both sign it, the judge signs it, and it goes into affect, but stay on your guard, because they will break it just to keep the drama and anger going. Which is exactly what happened to us, our agreement was broken in less than a month, however, the violation was not upheld in court due to ambiguity in the agreement even though it was a clear violation.
In other cases, sometimes it just takes a good mediator to get the two sides talking. If you are all reasonable people on opposing sides of a specific issue that you are both taking very seriously, a good mediator can get it out in the open and help you navigate through talking about it in a productive manner and perhaps reach a successful resolution you can both live with.
At the end of the day the chances for success lie in the hands of the parties involved and their willingness and desire to come to a resolution everybody can live with.

