Nick mentions this in the first couple of pages in introducing the book. He specifically cites the fact that a moral code was of value to him, and Gatsby did something to horribly destroy that.
So, in terms of Nick's character, he likes to stay under the radar a little bit and just watch everyone else. He tells us he doesn't really judge people, and then uses judging language. For Nick to discuss the fact that Gatsby doesn't fit that moral discipline that Nick would like to see is now almost unfair because we can tell Nick too, is flawed.
What about Gatbsy's career drives Nick a little crazy. When Nick gets the chance to meet Wolfsheim, Gatsby offers Nick a little business proposition. Learning that Wolfsheim participated in fixing the 1919 World Series, Nick declines Gatsby's offer and seems to be sickened by the entire meeting. This clarifies for Nick that because Gatsby is associated with this man, he must be doing shady dealings also. Nick also catches Gatsby in lies, but does not confront Gatsby.
Moral problems like not legitimately earning your wage, and lying about where he is from and what he has done both earn Gatsby a poor grade in Nick's school of morals.