If you mean by "unreliable narrator" that Nick Carraway is not objective and that his narrative is tainted with his subjective preconceptions or ideas, then there a number of examples.
The first quote is from chapter 1:
"When I came back from the East last autumn I felt that I wanted the world to be in uniform and at a sort of moral attention forever; I wanted no more riotous excursions with privileged glimpses into the human heart. Only Gatsby, the man who gives his name to this book, was exempt from my reaction — Gatsby, who represented everything for which I have an unaffected scorn."
The highlighted sections are a clear glimpse into Nick's thought processes and his prejudice. He wanted the world to be a place with more structure and discipline, a world of high values and morals, which means that if he did not find these in the characters and events he encounters, he would be scornful or dismissive of them. This is further supported by his statement that, even though Gatsby represented everything that he disliked, he refused to judge him. The irony here is that his opinion of Gatsby is exactly that--a judgment.
Nick's statement implies that his assessment is not objective or open-minded at all, so, as a narrator, his storytelling will be stained with his own perceptions. Since he will then not afford the reader to make a personal judgement based on his open and objective presentation, he is an unreliable narrator.
Another quote which clearly shows Nick's affinity for Gatsby and therefore his subjectivity, is contained in the lines:
"It was one of those rare smiles with a quality of eternal reassurance in it, that you may come across four or five times in life. It faced--or seemed to face--the whole external world for an instant, and then concentrated on you with an irresistible prejudice in your favor. It understood you just so far as you wanted to be understood, believed in you as you would like to believe in yourself, and assured you that it had precisely the impression of you that, at your best, you hoped to convey."
All of this just from a smile! The lines indicate how much Nick was affected by Gatsby's charm: he would, throughout the novel, describe Jay Gatsby in the most glowing terms, casting aside the fact that he was a criminal and adulterer, a man who would do anything to indulge a romantic ideal.
Finally, Nick tells Gatsby in chapter eight that
“They’re a rotten crowd,” I shouted across the lawn. “You’re worth the whole damn bunch put together.”
This emphasizes his derision for all the other characters he has encountered throughout the novel. He has only an "unaffected scorn" for them, and this has put an undeniable blemish on his ability as a reliable narrator.
In Fitzgerald's The Great Gatsby, one of the classic quotes that shows Nick is an unreliable narrator comes at the end of Chapter 8, when the last thing Nick says to Gatsby is, "They're a rotten crowd. You're worth the whole damn bunch of them put together." This shows that he is unreliable, not because what he says is untrue - we don't know that. Nick is considered unreliable because he is so involved emotionally in the events of the book, that he often makes statements showing his bias.
Two other examples of this bias are in the last chapter. In one example, Nick mentions that he wants to go home (back to the Midwest) because he really disliked and was put off by people in the East. This is an example of an unreliable narrator because it colors the reader's view of the situation.
The final example of Nick as an unreliable narrator is when he mentions that he doesn't even want to touch Tom to shake his hand, because he fears Tom had something to do with Gatsby's murder. This severely colors the reader's view of Tom and the whole situation of Gatsby's murder.