How do you keep from getting such ragged lines like the blue one in my sample photo. Ya I know there are body curves and thats why the logo of the dancers distorted. but the blue line looks like I scribbled it on.

If you map the UV template onto the figure, render and print, you will get a much better idea of how the lines fall. I ran into something similar when I drew my Aladdin Sane texture for Mike2.

Coppula eam se non posit acceptera jocularum.

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But knowing why you get this sort of distortion doesn't make it any easier to fix it. Presumably there is a way of drawing lines crooked on the texture so that they come out straight in the render. But how does one do this?

Phantast, as I said above, map the UV texture onto the body, render the figure, then print it out. You then have a guide to see where the lines fall. After that, it's kinda trial and error - and lots more rendering and printing - until you get it right. If you leave the UV gridlines on the texture until the very last thing, you have a constant guide to work to. Basically, the only way to do it is to actually dive in and do it.

Coppula eam se non posit acceptera jocularum.

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Well, that's what I mean, really. Trial and error is not a very efficient process. Looking at the example above, I'd have no way of guessing to put in a kink >there< and not there.