Clumsy Sarcasm
Say things like 'Of course I could be just as wrong as you.' Or 'Well naturally I'm not as subtle as you are, I don't know how to pick words apart until there's nothing left.' Or 'Certainly, you're right and the rest of the world is wrong.' Or 'Where did you read that, TV Guide/The Sun?'

Go Ahead, Contradict Yourself
Don't be afraid to make two mutually incompatible statements in one sentence. For instance, if you are a bishop, declare that the Church is not afraid of critical examination, but at the same time guards the 'truths' of its faith very jealously. If anyone asks how you can do both of those, exactly, just look vague and perhaps hum a little sacred music.

Pat Yourself On The Back
Say things like "This is a trivial issue, there are much more important battles to fight," and then go right on arguing. That way you give yourself credit for having a sense of proportion but still get to go on trying to win the argument.

Pave With Good Intentions
Make it clear that you mean very well, that all the benevolence and right feeling and compassion and tolerance are on your side, and all the other thing on your opponent's.

Repitition
If your ideas are weak, if you have neither logic nor evidence to back them up, simply keep asserting them over and over and over again. This will convince everyone that they must be true. If they were not true, surely we wouldn't keep hearing about them all the time?

Say The Methodology Was Flawed
When your opponent presents evidence (and it always happens, so be ready) that would undermine or completely contradict your argument, simply say everyone knows the methodology of that particular study was deeply flawed. Never mind if you know nothing about it, that this is the first you've heard of the study, just say they went about it in quite, quite the wrong way. If there's another study with a different methodology that also proves you wrong, no matter, just say it again.