Sorry, just seen this, wasn't ignoring your question. I don't really understand what you mean by addressing his arguments (eg he says he believes in Dave Brailsford, how do you address that statement in anything other than a pantomime 'oh no he doesn't', 'oh yes he does' style?), but the response below is what I 'think' about the whole thing, that hopefully goes some way to answering your question.
Honestly, I think (from what I've seen of it parsed through these boards, as I haven't read the book) that Walsh's writing is very interesting, and gives me pause for thought.
I choose to take what he says at face value, in that I think he probably genuinely believes what he is writing, and it's very obvious that as a result of spending lots of time with the team he has gone from being cautiously sceptical about their cleanliness to a true believer in it.
That, in and of itself, isn't enough to convince me personally that Sky is clean (because why would it), but it is an interesting 'dot' of evidence as far as I'm concerned.
And it's interesting because it then begs the question as to why he now is a true believer: he could be cynically lying about the whole experience (which I personally dismiss as just too far-fetched a possibility, but of course I could be wrong), he could be being made a complete patsy by team Sky or Froome himself (which, if they/he are/is doping, is the obvious thing for them/him to do, and I certainly don't dismiss), or (whisper it) it could be because they are clean and that spending 10 weeks with them is enough to form that judgement from one's observations (which again I don't dismiss).
Also, leaving aside the 'quality' or truthfulness of Walsh's argument, as a separate note I actually have a lot of respect for him for having the courage of his convictions/brazen cynicism (delete as appropriate) in this case. I actually think it would have been easier for him to project a veneer of objectivity as Skidmark so eloquently laid out, but that doing that would actually have been fundamentally dishonest - it would have been covering his own **** in case in 1 week/month/year/decade it all blows up in his face and his reputation would be left in tatters (at worst he'd be shown as part of a cynical fraud, at best a blithering idiot who Sky made a fool out of (see Armstrong/Ligget)). As it is, he has laid his cards on the table - and whether you think it's a winning hand or not at least (I tend to think) he's been honest about what he thinks.
Of course, since I don't know Walsh, I don't know any one from team Sky, and I have no way of forming any kind of meaningful judgement that goes beyond my own prejudices, suspicions and hopes I remain open to all eventual possibilities.