Nick Carraway is the voice of moral authority in the novel. His interpretation of events forms the heart of the novel, and his final moral judgments become ours. Fitzgerald lays the groundwork early to establish Nick as someone we can trust. He is a Midwesterner from a respectable family. He fought honorably in the war. He went East to begin a career through work and study. His family financed him for a while, but he was not given a blank check; his family expected him to work hard, succeed, and assume responsibility for himself. Even after being caught up with Tom, Daisy, Gatsby, and Jordan in the summer of 1922, Nick goes to work each day. (Only he and George Wilson, interestingly, actually demonstrate a work ethic and work through necessity.)
Fitzgerald makes a point of casting Nick as someone who by nature is not a judgmental person; therefore, when Nick does render a scathing opinion of the Buchanans at the novel's conclusion, his judgment is especially meaningful and trustworthy.
We can also trust Nick based on what he does, as well as what he says. He behaves in a decent manner. It is Nick who assumes responsibility after Gatsby's murder:
. . . as he [Gatsby] lay in his house and didn't move or breathe or speak hour upon hour it grew upon me that I was responsible, because no one else was interested--interested, I mean, with that intense personal interest to which everyone has some vague right at the end . . . . I wanted to get somebody for him. I wanted to go into the room where he lay and reassure him: 'I'll get somebody for you, Gatsby. Don't worry. Just trust me and I'll get somebody for you--'
Because of Nick's moral decency, in contrast to the amorality of the Buchanans, it is reasonable to infer that we are to trust him. If Nick's interpretation of the events of that summer and of the tragedy of Gatsby's life is not to be trusted, then Fitzgerald would have developed no theme at all in his novel. This seems implausible, especially when considering the novel concludes with Fitzgerald's beautiful coda expressed in Nick's words.
It is difficult to trust a character like Nick because of he is not the original source of the information that he presents to the reader. Nick is a "reliable" narrator in that he passes the information that he receives on to the reader but we can not be sure that the information that he gets is truthful. For example, everything that he knows about Gatsby up to the end of the novel when Gatsby father arrives is completely inaccurate; if Gatsby's father never showed up all of the information that Nick gives us about Gatsby would have been inaccuarate. Therefore, Nick thinks that he is reliable but is only as reliable as the sources that he is getting his information from.
You cannot always trust nick as a reliable character, his judgements are often corrupted by his feelings and relationships with characters. For example he percieves Myrtle as a thickish woman, she may however, not be a large woman but compared to the fragility of Daisy and the fact that this is the woman he dislikes he may show her as 'thickish'.
I think you cannot be justifyed in saying that Nick is a trustworthy narrator as although his father told him never to pass judgement, later he does exactly that. He is firstly just trying to set himself in a good light however, later he contradicts himself by passing judgement on that.
You also have to remember that Nick is recording the events 3 years after they actually occured, it is unlikely that he can remember the words themselves and what they say in the book is probably tinted by his relationship.
you can trust Nick because of his good manner and morals. Fitzgerald presents him as a good character .All characters in the novel are corrupted by money and misunderstanding of the American Dream except for Nick.