What problems do money and ambition create within the society depicted in the novel?
Much competition arises from the money and ambition of varying characters.
Take a look at Tom: His money is old. He doesn't have to work for it, he just has it. He lives his life as an arrogant man having his wife and mansion in one place while his mistress accompanies him to weekends of fun times in New York City. He has servants, he shows Nick the entirety of their georgeous property, he rides horses for fun, and he is stinkin' filthy rich. This has made him self-centered, self-serving, and uncaring to his wife.
Take a look at Gatsby: This man may have had an honest life in any profession, but because he thought he knew money would earn him a relationship with Daisy, he pursued it like crazy, to the point of illegal activity. I don't know where you are in the novel, so I won't spoil it, but Gatsby's rumored to be a bad man in some ways, and in one way, its entirely true.
This issue becomes the central one in the novel. It seems that Fitzgerald is suggesting that within a setting that placed such a high value on money and material wealth, there is often a very shallow pursuit of the good that follows. The entire atmosphere is predicated upon this. Gatsby believes that he can "win" Daisy over on the basis of wealth. The more lavish parties he throws, the more ostentatious his display of wealth, and the more abundance of material prosperity he displays enables him to believe that this will win her heart and passions. At the same time, Daisy, Tom, and Jordan are driven only by money and the desire to gain material prosperity. In the final analysis, money and ambition helps to create a false consciousness in which individuals' value is determined by the acquisition of wealth.
The major problem that money creates in this story is the problem that Gatsby has with Daisy. Her love of money and the comforts it brings makes her unwilling to go with her feelings and marry Gatsby back when she met him in Louisville. Instead, she marries Tom, which causes her more problems -- she becomes trapped, in a way, in her marriage because of her desire for money.
Gatsby's desire to get Daisy to love him then turns into an obsession with money that makes him do illegal things.
Money also seems to make most of the characters seem empty. They waste their time going to parties like Gatsby's that have no real meaning or value.