I love the idea of a podcast about technical writing. I would almost certainly listen to it.
As to methods of recording, those are many and varied. It's probably a matter of trying a few methods and seeing which produces the best result with the least amount of effort. I know some podcasts record everyone's audio separately, then combine it but that's a lot of work. Others prefer to use a Google Hangout or similar and put it as just as it was recorded. I listen to many podcasts where audio quality does vary a little but there are none where I think it's horrible. Some are more amateur than others, but otherwise they're all OK.
Before getting tied up in recording details, you also ought to detail the format of the show, what you aim to achieve, number of hosts and other details. Perhaps there are podcasts in the sort of style or format you're thinking of creating? If so, mention them so people know just what for what you're aiming.
Once these details are sorted out, go ahead and do some recordings, then get feedback. Consider them test shows, never to be published.
There are many others things to be considered but I thought I'd mention just these, rather than rambling on.
In short - I love the idea and would welcome the addition of a Write The Docs podcast.