general commodity production does have inner contradictions, at the most abtract level between social production and private appropriation.
Because the social relations of production are organized through commodity relations, prices must be governed by values for a society to achieve the proportional deployment of labor needed for its reproduction. But general commodity production is also capitalist or private production, the production of commodities by means of wage labor for profit. This latter systemic feature motivates capitalists to search for the highest profit, leading tendentially to an averaging of the rate of profit. But the averaging of the rate of profit contradicts the law of value if there is interbranch variance in capital intensity.
Marx in fact emphasized this contradiction; he thought Ricardo had glossed it over.
The question then becomes what is the consequence of this contradiction: it is of course the emergence of prices of production, which are modified values. Marx's derivation of the category of price of production is thus dialectical though this has not been argued in the same way as I have here (I am drawing from Ilyenkov though); it is also dialectical in that the emergence of prices of production also gives rise to a new phenomenon--the making social of the class antagonism as the surplus value is produced by the working class and shared out by the employer class as a whole (Geoffrey Pilling makes this point).
The point is that Marx's derivation of the category of the price of production results from studying the consequence of the mutually incompatible demands of one and the same system,