OK, here's my contribution to the Brain Stab "How to Argue More Gooder" project, consisting of the single most important thing I can think of to avoid bad arguments.
I'd like to say it was the first thing I ever learnt in a Philosophy class, but that's not true -- it was in Stage II Ancient Greek Philosophy. I still have my old notes, and there it is:
Aristotle says: "BEWARE OF EQUIVOCALS!"Beware of equivocals. BEWARE THEM! Beware them like you would the Ides of March. Equivocals are what you get when you're using the same word to mean slightly different things. In the context of the bit of Aristotle that we were studying at the time, he's talking about how "being" is equivocal -- the "is" in "Josh is human" means something different to the "is" in "Josh is sitting at his desk". Sometimes it really does depend on what the definition of "is" is (although it didn't when Bill Clinton really wanted it to).
At any rate, in the vast (VAST) majority of cases I see where people are disagreeing over something, it's not that one side is flat out wrong, it's that both sides are using the same word differently, and neither realises it, resulting in the sort of "talking past each other" scenario that Eric mentions in his post below.
The Perigo vs. Nola debate that he highlights is the perfect example. Frankly, I couldn't stomach reading all the way through to the end, but it all started with Perigo objecting to Nola's statement that "logic has nothing to do with reality". Now, Nola was using "logic" to refer to the abstract symbolic systems that describe the relationships between propositions; systems which, being abstract, have no immediate relation to the real world, and must be combined with real world facts to form a meaningful argument. On the other hand, Perigo seemed to understand it in a more colloquial sense, where "logic" is used as a synonym for "reason". Under Nola's definition, it's true that "logic" has nothing to do with reality; under Perigo's, that's not true at all. However, Perigo doesn't seem to notice the equivocal at all, and Nola does a piss poor job of explaining it.
Bonus argument tip: Consider your audience, and put things in a way that they will relate to. Nola makes the mistake of talking like the member of a Philosophy department to an audience hostile to academic register of Philosophy departments, as does our Morthos when trying to discuss the Free Will vs. Determinism controversy on Peter Cresswell's blog (see Eric's post for links).
Sometimes it seems that philosophers are obsessed with definitions (Aristotle particularly so), but this is why -- you need to be really sure how everyone's defining the words they're using, to make sure that equivocals aren't cropping up and buggering everything up. BEWARE THEM. Bewaaaaarrrre...