It’s useful to distinguish two different kinds arguments, which Marx develops in his writing, each of which is a criticism of capitalism:
(1) Arguments about what makes capitalism despicable and worthy of resisting. This is only modestly novel; the basic dissatisfaction with capitalism is not uniquely Marxist. He and Engels elaborate it and refine it along a certain line.
(2) Arguments about what will destroy capitalism, or how a post-capitalist society will be brought about. This is more novel and what is ultimately meant by “Marx’s critique of capitalism.”
Marx argues, in effect, that human beings are essentially social and productive, or co-creative, beings. Hence, the highest expression of the human essence would consist in spontaneously and freely contributing to the cooperative reproduction of society and the creation of culture.
Within capitalism, however, all production is undertaken for the sake of producing profits and wages. From the capitalists’ perspective, production or service is maintained only to the extent that it continues to be profitable. Workers, meanwhile, engage in production or retain employment only insofar as they obtain wages. Wages are the price of commodified labor, as determined by the market. Profits are the surplus value derived from commodified labor. Hence, capitalism is perverse in that it renders that which is essential and intrinsically good (production and creation) as accidental and instrumentally good (a means to make money).
Moreover, it is alienating in that it induces us to seek our essence in alienated form, i.e., in the form of money. People in our society often scoff at this notion, but I think there are reasons to suppose the point is actually more widely accepted than is acknowledged. For example, many people dream of and seek to become entrepreneurs. Presumably, this is because they want to engage in a relatively less unalienated form labor; that is, they want their work to be a more immediate expression of their creative and productive capacities. And to add to this, they ultimately aim to retire as early as possible so they can engage in productive work (hobbies) free from the demands of profitability.
In short, Marx maintains that capitalism is what will destroy capitalism. The reasons for this are as follows:
Capitalism produces the proletariat, or the class of non-owning laborers. The interests of the proletariat are in conflict with the interests of owners.
Capitalism is crisis prone, regularly resulting in recessions, which result in under-consumption (i.e., poverty, starvation, death, and the misery of those in the exploited and expropriated classes).
Capital tends to become concentrated or controlled by an ever dwindling number of owners, owing to competition.
The proletariat has the unique capacity to be a world-historical agent of change. As the proletariat increases in number and becomes increasingly subjected to the exploitation and misery associated with under-consumption, its liberation from the system would constitute the liberation of (the vast majority of) human beings.
However, the proletariat must become self-conscious. They must understand the systemic causes and effects of their oppression, as well as their capacity for world-historic change.
In relation to the first point, in the Communist Manifesto, Marx and Engels wrote,
“The development of Modern Industry... cuts from under its feet the very foundation on which the bourgeoisie produces and appropriates products. What the bourgeoisie therefore produces, above all, are its own grave-diggers. Its fall and the victory of the proletariat are equally inevitable.”
Anthropological Thesis: Human beings are essentially creative and productive in the sense that we must actively (re)produce our means of subsistence.
Development Thesis: Productive forces (i.e., the means of production plus embodied knowledge of their employment) tend to result in an increase in productive capacity. (They might fail to, but that’s the “trajectory”.)
Determinism Thesis: A society’s economic structure is determined by the level of development of the productive forces, and its political and legal institutionsbare determined by the economic structure. (Now: “determined” literally means constrained or directed; it does not mean fated.)
Conflict Thesis: As productive capacities expand, the limitations of existing economic and social structures result in “contradictions,” or instabilities; they fail to harness and direct productive forces. (Consider massive levels of unemployment relating to automation.)
Revolution Thesis: When an economic structure constitutes a fetter to productive forces, it will be revolutionized and replaced with one that does not so fetter the productive forces in their present state of development.
While Marx is explicitly and vehemently not a utopian socialist—such forms of socialism are idealist, not materialist—he does identify some strategic goals and features of a social-political order that would better fulfill the promise of the French Revolution (namely, the achievement of equality, solidarity, and liberty):
Workers should collectively seize both the means of production and the apparatus of the state. Marx recognized that he was calling for a revolution, i.e., a suspension of the rules (esp., property laws).
Democractic self-determination - all officials should be elected by the workers from their ranks at regular intervals, paid an average worker’s salary, and be recallable by the workers as they see fit.
Democratization of the economy - production should be democratically planned and coordinated to meet human needs and desires, not blindly guided by market-determination and the profit motive.
Capitalists and their economists usually do not disagree with Marx on these points, though they may be loath to admit it:
Capitalism is crisis prone, i.e., prone to oscillating between periods of contraction (recessions) and expansion. Indeed, done economists try to predict these cycles.
Recessions result in human misery.
Capital tends to become concentrated as result of competition and buy-outs. (Antitrust laws and taxation schemes seek to curb this problem.)
The chief points on which they usually object:
The interests of capital and the interests of workers conflict.
Rational planning of the economy would result in better outcomes than a market-directed economy.
Some matters are not objected to per se, but only in their proletarian form:
Revolution - bourgeois revolution is okay. (“Spreading democracy” and overthrowing political regimes is fine so long as it opens markets.)
Democracy - bourgeois liberal democracy is okay, but there need to be checks or stumbling blocks in place to ensure that there isn't genuine rule by the majority of the population, and especially not majority rule rooted in class interest.
Class Dictatorship - bourgeois dictatorship is okay, just not working class dictatorship. In a de facto sense, we do have a dictatorship by the monied interests.