While I feel this is deviating from the topic at hand, I have always had some questions about how a society could be classless. Even a kindergarten was made into a class society based solely on eye color after the teacher mentioned that eye colors meant certain things about a person. In a communist society, even if wealth were equal, there are many inherent factors that differ between people due to their unique genetics and life histories. Consider just charisma and attractiveness. Someone who was rich in both would still be in a vastly superior position compared to someone who lacked both, and would be able to secure themselves an overall better life (at least on average). The only way I could see full equality of outcomes would be with some power in charge directing it, and even then the one heading that power would still be superior.

Consider something else, reproduction. While not all people want to have children, it is a major desire of many people. How do we ensure equal opportunity of reproduction to all who wish to have children?

The kind of class Marx was referring to is that of economic class, that is, class created as a result of the relationship to the means of production. Marx's view was that throughout history, various groups of people have definitive relationships to their means of sustenance - that is, who provides for them, so that they survive? In slave society, it was the slave master providing to the slave, for example. In today's society, the largest group of people, the proletariat, sustain themselves via the bourgeoisie employment in the form of wage labour.

I do not think that Socialism itself does away with the problems of humanity, but it does away with the power relationship between proletarian and bourgeois, and also all those other historical classes.

Communism isn't about equality of outcomes, it's about having the ability to apply your labour in the way which you are able to, in order to provide for yourself. Of course we must work to live (which is unfortunate, but Socialism helps mitigate that by voluntary means). It is totally fine, in my opinion, to have more than the other person next door. In a Communist society, the only reason why you would have more is because you worked harder, put more hours in, or were more efficient at what you do than the other person.

With regard to children, I don't know how to answer that question, and I don't know if there exists such a way by voluntary association which leads to such an outcome as perfect equal opportunity for reproduction. I would be very interested in finding a way, though.

Well, this is the basic problem. Marx and Engels had a vision of society governed by the better angels of our nature, not to mention a relatively simple economic understanding of the world due to the technological limitations of their day.

Karl Marx died in 1883 so while he was probably able to make guesses about how steam engines would be deployed in the future he never lived to see an actual automobile. Adam Smith's economic insights were likewise somewhat limited by the technology of his day; one has to be careful not to attribute knowledge that we only enjoy with hindsight to economic theorists of earlier eras.

I don't think that most of Marx's analysis of capitalism falls flat in the face of modern developments; some of it of course do (such as his theorised 'Asiatic mode of production' which didn't exist) but for the most part I think a Marxian analysis is a cogent one, at least from what I've seen. Marx was in a good position to envisage how technology would develop, having seen the result of the industrial revolution himself. Marx intended for his analysis of capitalism to hold regardless of time frame; arguably, and indeed into the future beyond capitalism taking the form of the theory of historical materialism.