There are several errors in Marxism, here are some insights as follows.  

The first error is his assertion that another person’s gain must come at another person’s expense is a myth.

This thinking is based upon scarcity.  It views the earth as a pie. It also comes from the sin/curse nature that fosters evil in competition, jealousy, envy and coveting. Truth is one persons gain brings gain to all.  God has created more than enough for every person.  Wealth is not a pie. Rather an inexhaustible river, and with each person adding to the tributary by their own supply and demand. There is room for all to raise their standard of living through innovation and productivity. It is perfectly feasible for multiple parties to compete and do well in a market of consumers who want their goods and services.

The second error, Marx was wrong in his belief that the value of a product is based on the amount of labor that is put into it. 

Jesus speaks to this a bit in Matthew 25, as he mentions that each have a different level of talent.  Each person creates and manages according to their ability.  Each person has a different ability.  Some are more skilled due to school, experience or inherent talent. Secondly each person has a different level of passion (motivation) for work and the application of our talent.  So not all produce at the same level.  The value of a good or service simply cannot be determined by the amount of effort a laborer expends. For example, a master furniture maker can more quickly and beautifully make a piece of furniture than an unskilled craftsmen can, and therefore his work will be valued far more (and correctly so) in an economic system such as capitalism.

The third error of Marx’s theory of socialism necessitates a government that is free from corruption and negates the possibility of elitism within its ranks.  

If history has shown anything, it is that power corrupts fallen mankind, and absolute power corrupts absolutely. The only King who is pure is Jesus.  This is why He must rule and bring every king into subjection to Father. This is why governments must follow the model of the King, who did not come to be served, but to be the chief servant.  Prime minister means chief servant.  Jesus declared he who wants to become great must become the servant of all.  

Only by following Him can a culture bring forth a selfless government. People do not naturally become less selfish.  A nation or government may kill the idea of God’s ways and decrees as a the foundation for government, but when that happens a person will take God’s place in that government. That someone is most often an individual or group who begins to rule over the population and seeks to maintain their privileged position at all costs. This is why socialism has led to dictatorships so often in world history.

Fourth and most importantly, socialism is wrong. It teaches that a person’s identity is bound up in the work that he does.  

Your value is much larger than the work you perform.  Although secular society certainly promotes this belief, the Bible says that all have equal worth because all are created in the image of the eternal God.