The first is that the Federation is but one of many interstellar powers within its galaxy, and that's putting aside any of the thousands of unaligned or independent worlds and smaller coalitions. Many of these societies, even some of the Federation constituent societies, appear to use their own currencies or means of exchange. Take the Ferengi as the most extreme example. They are basically an anarcho-capitalist society, bordering on kleptocracy. Money is important to the Ferengi, to put it mildly. So how does the Federation conduct trade with the Ferengi government? On a more microeconomic level, what happens when Bashir and O'Brien order a couple rounds at Quark's? Who picks up their tab? Clearly Quark pays for his own supplies, and charges hefty markups, and he's always seen fretting about the difference. I have a hard time believing that Federation officers can just consume his (clearly limited) resources without contributing to his profit margins. And if they pay him in Federation Credits, what good are they to a non-member of the Federation? If they are not currency -- if they are more like scrip, or rations, or promissory notes good for X units of energy, or what have you -- then this creates a serious problem for Quark. Presumably, the value of Federation credits is relatively fixed and/or tied to some other unit or commodity. It is not a fiat currency. So why in the world would Quark accept credits, when he'd strongly prefer latinum? And how does one go about exchanging one for the other? For that matter, what would the Federation make of someone who decided to exchange all of his credits, even if he could, for gold-pressed latinum? If credits are not money, then perhaps they are something along the lines of notes or bonds, floated by the Federation government. In which case, Bashir and O'Brien pay for their drinks in the equivalent of US treasury bills, or perhaps in fractional shares of a Federation sovereign wealth fund. Or perhaps they are energy rations of some sort, in which case, Quark needs energy as much as any other business, and so he's happy to accept it (and to charge as many energy-units as he sees fit for his food, drinks, and games of chance).
The second problem has more to do with using Starfleet as the lens through which we draw conclusions about Federation society. If I were to show some alien society a documentary about the United States, set primarily on a US aircraft carrier, with ~90% of the situations and characters taking place in a military context, my alien viewers would draw some very interesting inferences about the US (or, more broadly, all of human society). They'd think we were a rigidly hierarchical society. They'd think we have a handful of basic professions, and that nobody really cares too much about personal property. They'd wonder how everyone gets by, and how resources are allocated, and they'd probably assume it's through a quasi-socialist system of rationing and stipends.
The microcosm of the US military is different from the macrocosm of US society, and especially different from that of the entire world. It's sort of a mini society within a larger society, operating under its own rules and organizing principles. Similarly, we should suspect that life in Starfleet is probably different, in some meaningful ways, from ordinary life in the Federation. And life in the Federation is different from life in the Klingon Empire, or in the Cardassian Union, etc.
None of this is to discount the deep and insightful thinking on the part of this article's author. Nevertheless, I think we should consider the limitations of the framework through which the shows allow us to view the Star Trek universe. We get our fair share of glimpses into the outside-Starfleet world, but we should still be mindful of the observational lens through which we catch those glimpses.