Bad things happen, so the discussion should include response as well as avoidance.  Sometimes the best response is for the RO to get to the jury desk before the competitors and request redress on their behalf.  The competitor's response to that action may be to cut the RO some slack for the rest of the regatta.  Happy sailors party; unhappy ones protest.  :-)

Managing OCS calls poorly will give you a lot of time in the room.  And if you 'lose' an early OCS redress request look for lots of continuing business as the regatta unfolds.  So well-managed starting procedures are the first step towards fewer redress hearings.  After the starting signal you are ever more dependent on the competence of your mark layers ....

I’ve got a few that I’ve been collecting over the years:

In my opinion, good communication, humility, and solid preparation and procedures are your key to success. If you are friendly in your communication and have a collaborative attitude with the fleet, they will cut you a lot of slack. If you are quick to own up to mistakes and make them right, you will have a fleet full of friends. My best practices include:

1. Start every day with a "welcome to today's racing" statement to the fleet. Explain what you see in the weather and what you expect to happen for the day. Offer time for questions. Starting the day with a positive statement makes everyone think you are on top of it. 
2. For OCS calls, I ALWAYS tell my fleets that if they think there is an issue, please come talk to me before you file for redress. We can listen to my audio recordings before we go any further. Listening to the tape solves most issues, especially if you are using the "Hank Stuart" method of talking through locations of boats relative to the line in the minute leading up to the start. 
3. If you make a mistake, own it. Apologize, then do your best to make it right. If something you did caused disadvantage for a boat and you know it, then file the redress request on their behalf. Even when you know there isn't a likelihood of success, you are now on their team, not the other way around. If you know you botched the OCS calls, go to a general recall and start over. Last year, I accidentally grabbed the RC channel VHF, not the competitor Channel VHF. As soon as I realized my mistake, I went to general recall. I explained on the radio that I had messed up and in the interest of fairness, I am going to start it over. The first thank you came from the guy who had won the start. They totally understood and appreciated the prioritization of fairness for all the boats. 
4. Don't hate the redress room. Be friendly and offer your take on things. I always use statements like, "We saw the mark moving. I asked my mark boat to get there and fly the M flag. I think it took them 2 minutes. I'm sorry we couldn't immediately get there and I wish that happened faster. If you as Jury deem that as an improper act, then the sailor(s) deserve redress." If you aren't fighting it, the hearing will go faster and the fleet won't be angry. 
5. Develop your team. Be a coach and mentor. Start your morning meeting with discussion of a problem and how we will solve it as a team. Some days, you will have an example from the day before. Some days, create a hypothetical like the mark moving. 
6. If something happened yesterday, explain it to the fleet and explain how you plan to do better. Ask for feedback, even if you have a good plan. The competitors are REALLY smart. If they feel like you are working with them to run great races, then they will cut you all the slack in the world when things go wrong. 
7. Be friendly at the parties. Talk to the competitors. Ask your team to sit with the sailors, not each other at dinner. Be approachable and if someone challenges you, be humble and friendly. 

I guarantee that if you take these steps, everyone will have more fun, including you. If you go to the redress room, it won't feel like a burden. 

Finally, consider this:

Which is worse? 

a. Sailor is OCS and asks for redress. The RC and PC are disdainful and act as though the sailor is doing something wrong. The redress is denied and the sailor leaves angry. Maybe they don't come back next year. 
b. Sailor is OCS and asks for redress. He meats with the PRO, listens to the tape, thinks there was a problem, and files for redress. In the hearing the PRO explains what happened, offers a sympathetic tone and apologizes that it wasn't done better. The PC explains that while it wasn't ideal, it doesn't meet the burden of "through no fault of your own" and we can't give redress. The sailor leaves disappointed, but doesn't hate everyone in the room. They come back next year and you enjoy dinner together because you apologized and didn't fight your mistake. 

The best way to avoid redress is don't confuse the competitors.  "Don't be tricky" - Luigi.  "If you think you got away with something, you didn't" - Tom Duggan.

In general, I agree with everything John Porter has said. Own your mistakes.  I've even filed redress for the competitors while I was still on the water (fill out the form, photo, email to jury).  That gains a lot of respect with the competitors.

And lastly, the RC never "wins" or "loses" a redress hearing.  If you made a mistake, own it and the competitor(s) deserve redress.  If you didn't - and you've got the documentation to back yourself up - the competitor probably doesn't deserve redress.

I have spent a lot of time either managing or judging offshore and oceanic races where redress cases are mostly about actions by sailors giving assistance under fundamental rule 1.1 

However redress is given it has to be justifiable.  There is always a tendency to reward boats and sailors that have gone out of their way to render assistance.  But rule 64.2 requires the protest committee to make as fair an arrangement as possible for all boats affected.  Is giving extra redress for undertaking a perilous rescue attempt fair within the rules?  I think not.  There are other ways of rewarding exemplary seamanship and conduct,

Finally, what happens when a boat complying with all the racing rules,  the international regulations for prevention of collision at sea or governmental rules is either stopped or delayed by the actions of a government or other official authority.  There is no provision within rule 62 for this to be considered for redress.  Yet boats are quite frequently stopped by harbour authorities, coastguard or other vessels when proceeding entirely lawfully.   In any offshore race where I am involved I add a rule 62.1 (e) An action of governmental or other authority.    Boats still have to comply with the requirement in the first paragraph of rule 62 that there shall be "no fault of their own.  

Naturally happy to debate further and give some practical examples of redress issues and calculations (as in the workshop I did for the RYA some years ago).  

I think the comments so far are right on target. Communication is the key - a coaches/competitors meeting in the mornings, a walk through the boat park in the afternoons, radio broadcasts of rc intentions are all key in the integration of sailors and race committee. I would add that pre-regatta conversation among race committee, classes and the OA is essential to understanding expectations and capabilities. In one design regattas, I always ask the class to designate a spokesperson to talk directly with the pro so that the sailors feel their voice is both heard and appreciated.

For a talk on “Race Officer and redress” I would discourage the attitude that redress hearings are about winning or losing. It is particularly important to avoid the natural inclination to get defensive or take redress hearings personally. 

I would approach such a talk on the basis that race officers deal with a lot of things out of their control. Redress should be regarded as an important way of rectifying competitors’ scores when appropriate when Appendix A5 doesn’t apply. At the same time, competitors should not be allowed to used redress as a way of getting an unfair advantage over their competitors. Those redress applications should be resisted because redress would be unfair on the fleet as opposed to being unfair on the race officer.

It follows that in redress hearings, a race officer should be honest, objective and informative. The more the protest committee can rely on a race officer’s information and trust them, the more persuasive they will be. Success in the room comes from building up trust.

Success in the room also comes from the quality of the evidence a race officer can present. That comes firstly from having good systems in place to acquire and record accurate information about the race. Secondly, it comes from mental discipline.

Good systems are a matter of foreseeing problems, being in a position to rectifying them, and then recording accurately what happened. The first two steps are normally considered by race officers and are the most important. They prevent redress hearings from occurring in the first place. But the third should not be forgotten.

Evidence should not only record that a mark moved, but how far? In what direction? What difference did it make to the competitors? Can you provide an accurate birds’ eye view of what happened? What else would a protest committee need to know? If you have to rely on the evidence of a mark layer, how reliable are their notes likely to be (if they exist at all).

Trainee police officers are told that for everything they say or do, imagine standing in a witness box in court explaining it to a judge or jury. That should be the same for race officers and all other people involved in race management. If a police officer deals with an assault, they will need to act quickly to arrest the perpetrator and arrange medical treatment for the victim, but they also need to take accurate notes and statements so the case can be presented in court. Otherwise there could be a miscarriage of justice.

So, look at the information available. How accurate is it likely to be? How well recorded? Is it accessible?  It is better to have less information that is accurate and accessible than a lot of information that is questionable.

Mental discipline is important. While there are a lot of things happening, it is important to avoid getting stressed and loosing the plot. A race officer’s performance depends on their mental state. 

In the context of redress, that means that while a race officer is acting, they also need to be able to stand aside and see things objectively. Put themselves in the shoes of the sailors and see how they are likely to understand and react to communications? Like the police officer analogy, how will you explain everything to a protest committee?

I fully agree with the comments in other posts about communicating and getting the trust of the fleet as well. That is obviously just as important as what I have written.

I like to suggest to race officers that they get experience sitting on a protest committee to see what it is like from the other side of the table – I would also suggest to judges that they get experience of what it is like working on committee boats.