Let me preface my responses with the caveat that I am but one man, and this but one man's opinion. How it would actually go down may be completely different.
What keeps violence from breaking out? Say if someone doesn't like how the arbitration goes, and he and his gorilloid brothers and nephews and cousins decide to take matters into their own hands.
Well, first, this is not a culture of victim disarmament. Taking matters into their own hands would also be taking their life into their own hands...or rather, their opponents' hands. Secondly, they would have signed a contract to abide by the arbitration decision, so doing so would breach that contract. There's lots of examples on this very site of possible solutions.
What keeps Snake Oil Shoppe from bribing Underwriters Laboratories to declare their drugs safe? If no one dies and only a few get sick and can't trace it back?
The other QA labs, for one thing. Competition keeps 'em honest. Secondly, you know that little tag you sometimes find in your clothes, "inspected by #16", and such? Well, imagine if #16 were personally liable if your pants somehow harmed you? The inspector who took the bribe and signed off on Snake Oil Shoppe's application would be personally liable for the damages thus incurred. No hiding behind corporate personhood, without the government creation of the corporation.
I suppose the question becomes one of moral accountability. You say that requiring corporations to be accountable to the people buying the goods and services is enough, and that a gov't is inherently not accountable to anything. I think it is more effective to try to build that accountability into gov't from what is already there.
Which brings me to my next point. Not corporate accountability, personal accountability, and competition. You buy bad dope, you, or your heirs (my condolences) take the dealer to task on it. Other people hear about that, and buy from someone else. This is almost how it works in the black (Konkin prefered the term red market to refer to illegal markets where violence is acceptable, and I agree.) market, except there's no clear way to determine exactly who cut your X with rat poison.