Nick is easy to relate to, in part, because he and his judgements are fallible. We can trust Nick's version of the facts, I think, but we cannot fully trust his judgements of the other characters in the story. He is biased.
Nick's bias leads him to deride Tom and praise Gatsby. Gatsby, for Nick, represents a fundamental innocence and honesty, despite the fact that his life is outwardly built upon a lie. It is inwardly built upon a boy's vision of the future, of personal greatness. This vision speaks to Nick even as he learns to abandon it for himself.
Yes, I trust Nick as an extremely objective, non-judgemental narrator for the most part. It is only until he encounters the most dispicable of behaviors, such as those exhibited by Tom, Daisy, Myrtle, Tom, and Jordan, that he really makes any sort of judgement. Saying that he's worth the whole damned bunch of them put together is a strong judgement, although a rather correct one considering the types of evil he observes. Whether it's a cheating husband, a cheating wife, a backstabbing friend, a friend of pure convenience, or a murderous victim of adultery, the behaviors Nick sees are those he cannot excuse. He does not embellish when he reports his observations; however, he does give a clear view of things going on that allows the reader to make up their own opnion before the story concludes.
I do trust Nick, and I think his judgments are sound. He certainly pegs Tom and Daisy for exactly what they are, "foul dust." I trust Nick because he never loses touch with his own identity, and he never rejects his own Midwestern values. He isn't sucked into the wealth and the glamour he stumbles into at West Egg. He takes it all in like a tourist in a foreign country, but he never becomes a part of it--nor does he try to, unlike Gatsby.
The "telling detail" about Nick Carraway is the manner in which he handled Gatsby's death and burial, with such decency and respect. It also says much about Nick's character that he is so shocked that Daisy acknowledges Gatsby's death in no way at all. Her conduct is so deplorable, Nick finds it hard to even comprehend, much less understand.
Nick came to New York to study and prepare himself for a new career--his family expected him to work for his living--but he is so sickened by what he has experienced there, he goes home. Even after getting back home, however, he can't stop thinking about Gatsby and what had happened to him. The fact that Nick has been so deeply affected gives me one more reason to trust him. He's a person of substance and integrity.
We are supposed to believe Nick because he is the narrator. He is the voice of Fitzgerald throughout the novel, and he is supposed to be believable. Through his eyes we see Daisy and Tom for who they really are. However, we should question Nick at times. He is a little too gullible when it comes to Gatsby and his "stories" about his life. Through his eyes we see Jordan cheat in golf. We see Tom break his girlfriend's nose out of anger, and we see Daisy flirt with Jay right in front of her husband. He is most believable through his first observations of each character. He describes them directly, and describes their actions word for word, so there is no misinterpreting what they are doing. Fitzgerald wants Nick to learn about moral corruption firsthand so that we can see it more clearly as well. Nick is a good man. He knows that Jay is also "better than the whole lot of them." Even though he is a little naive, he is humble and honest. He makes mistakes along the way, but he admits them. That's what makes him such a good character.