The first challenge in talking about market socialism is determining what precisely we mean by "market." In one sense, any time individuals have choices, and the exercise of those individual choices in the present has an effect on the options available in the future, we have a market. Since every kind of socialism worthy (IMnsHO) of the name wants to maximize human freedom, and an essential part of the maximization of freedom is that the exercise of that freedom should have an effect on society, all forms of socialism include markets. Thus, to be non-vacuous, market socialism must embed a more specific definition of "market."
We could define markets thus: We have firms and households. Households give tokens (money) to firms and receive goods and services; firms give tokens to households in return for labor. Firms that are more or less "efficient" at collecting tokens grow or decline; households that are more or less "efficient" at collecting tokens consume more or less of the social product.
We can add a lot more moving parts, but I think this definition captures an important sense of the market. (The above, of course, is not the only logically possible definition of markets. If you have an alternative definition, feel free to offer it in comments.)
At the social level, we don't have to micromanage everything: all we need to do is measure and manage the tokens. The whole point of markets is let the system "self-manage."
But just the broad definition above fails to resolve the fundamental contradiction of markets: at the individual level, markets entail that households and firms have an incentive to maximize "profits"*; at the social level, we want to use competition to minimize profits. Every household and firm wants to maximize its own profit and minimize everyone else's. This contradiction is not just perversity: it seems built into the whole concept of the market at the most basic level.
*We can broadly define "profit" and "efficiency" as the ratio of goods and services consumed to labor provided. Only households are profit-seeking in this sense; a firm is just a collection of households (or representatives of those households); these households use the firm to maximize their own profit. Depending on the social system, there might or might not be within-firm competition for profits, but by definition there is always between-firm competition for profits.
If we could impose market competition completely exogenously, markets might work. But, as Lenin argued in The State and Revolution, politics is endogenous. The households at firms that are "profitable" gain more economic power, which inevitably translates to power not only over the production of goods and services, but also power over the social systems in which firms produce goods and services. And if we structure the market give people an incentivize profit maximization, we are by definition giving people an incentive to avoid the competition that would reduce their profits.
This is not just me saying that no system is immune to perversity: the perversity is built right into the market model: the individual and social goals are exactly the opposite. And it's not really a "dialectical" relationship, because the individual profit-maximization incentive creates intentional action, whereas no individual has an incentive to encourage competition.
Radical democracy (as opposed to capitalist republicanism, which is at best weak tea and at worst a sham) might create some individual incentive to impose competition and make markets work. But still we have the collective action problem. A profitable firm, regardless of how it's run, has a concentrated incentive, its profits, can can act with unity to preserve those profits. In contrast, the incentives for maintaining competition are diffuse: no individual voter has very much at stake. A democracy is harder to hack than a republic, but nothing is unhackable, and where there's an incentive to hack, hacking will happen.
Worse yet, I'm just talking about setting prices for goods and services: things get even more dicey when we try to use markets for capital allocation.
I would have to see a much more detailed exposition (more detailed and thorough than the Wikipedia article) to buy market socialism.