While their claim about the world is certainly off:

1. 13th century is not what was being depicted in spice and wolf. It was a depiction of renaissance-era to age-of-reason mercantile trade.
2. the point to which they were specifically referring was the gigantic plot arc that specifically focused on the debasement of currency and speculation thereupon, the markets for which were almost exactly as described, you seem to be taking their word "market" to mean "physical space and event", when S&W examines basic market theory in a mercantile environment. Its depiction of economic speculation, debasement of currency, etc. Are nearly impeccable, aside from random bits like "make the fur smell like apples" (though I shouldn't put it past some random merchant to try such a ploy, even if i think it unlikely to avail them), even down to the "money changers clinking coins together to try to hear differing purities of silver", which you can do yourself with silver coins. While there are certainly many aspects which did not accurately reflect renaissance Europe, pretending that something has no historical basis because the costumes in a fantasy setting based on both Europe and Japan aren't period appropriate to a period several hundred years off of the period it's actually based on is absolutely ludicrous.

As far as organisation of the communities, you're absolutely right. Though, I can't think of a single work of fiction, ever, which accurately depicts the sheer level of societal interconnection in any period, so I think the criticism unfair, given how perfectly it nails the economic principles it tries to tackle.

As far as the local policing force, I'd like to see a source on the presence, efficacy and integration of local police forces in continental Europe during the renaissance. I am only familiar with London, but I distinctly remember that, at the time period roughly equivalent to that being depicted in S&W, London was barely into its "thief-taker" phase of policing.

Anyway, if you're judging Spice and wolf off of the first episode, then you're missing the entire first arc that the commenter is referring to, in which the show explores, in exacting detail, precisely the phenomena to which your original comment was referring