I think that Gogol is using this story to critique the flaws of the bureaucratic society that was created with the Table of Ranks.  Akaky is so involved in his government work that he has no time to experience life and in unable to do so because of the financial hindrances of his job.  That Gogol makes a point of discussing how Akaky was born for the job he has and remaining stagnant despite others movement seems to critique the harshness of legalized social status and emphasize the trap that is civil service.  Instead of striving to improve his situation, Akaky accepts his low place within the hierarchy and remains blow his peers.  One effect of the ranking system is that it seems to breed resentment between the different ranks, as the Important Person cannot bear to speak to someone lower than him and uses his power to criticize his employees.  The condition of civil service described in Gogol’s piece is akin to how one might imagine the conditions of serfdom, a “bureaucratic serf.”  The state is made strong at the disadvantage of the individuals that serve it.  The overcoat functions as a status symbol that endows Akaky with the respect of his peers and the confidence to step outside his closed world.

The Overcoat also seems to be a critique of materialism.  Akaky quite literally subverts his quality of life for the possession of a new good.  When he dies, Akaky is described in terms of his possessions, and the form that appears to him at death is a ghostly overcoat.  Even in death, Akaky is defined by an endless search for material possessions.  It could be possible that this anti-materialist sentiment was brewing in Russia at the time of print because of the rising imperialism and the promotion of nationality as folk identity in the face of modernization.