I would imagine from the original post that what we are dealing with is someone who, although they may have a valid complaint about organisation or services, will blow it out of all proportion and pursue it aggressively to the point of offensiveness.
I get a lot of these in my work. A number are aggressive people, rude people, sometimes because they are not articulate enough to understand their own issues.
The first thing I establish is what they actually want by way of a resolution, BEFORE they launch into a wild tirade, i.e. do they want their money back, are they trying to improve the system etc. This stops a lot of moaners in their tracks. The more they ask for, the more I stress I will need to investigate their complaint fully and independently in their absence.
Once I've established what their expectations are, I then listen to their complaints. If they shout or become abusive, I ask them to go away until they have calmed down to the point of reasonableness. I have an assistant who can remove them if necessary. As they go on, I distinguish subjective and objective information in the way I deal with each statement. If there is a factual problem (e.g. programme running late), I gather data ("how late? were people made aware of this as the problem arose?"). I deal more severely with subjective issues ("It was crap." "What qualifies you to judge the quality of this?").
I then have a list of their fact-based issues, plus their contact details. I tell them to go away and I will write to them once a full investigation has been conducted. I insist on no further contact with them until they have received my letter.
I ALWAYS send a letter, even where complaints are unfounded, simply to remove further ammunition. I keep a file of thank-you letters from those who feel I have done a thorough job.
Sorry if I'm teaching grandmothers to suck eggs, but the key aims for me are to establish their expectation, obtain facts (just the facts, ma'am) and to get rid of them as quickly as possible so I can get on with my job. I probably write one to three letters a day at busy times. I do not accept and will not put up with rudeness or offensive behaviour and have removed many people until they have calmed down enough to enter into rational discussion. Always have a witness present, preferably someone who can do the removing if necessary.
Hope this helps.