Whether readers think Nick Carraway is an unreliable narrator depends greatly on perspective. Many critics do think he is unreliable, while others do not. There are a few key parts of the novel which suggest that he might be unreliable.
The main thing that leads us to question his reliability in the first place is the fact that he states himself, "I am one of the few honest people I have ever known." When people are truly honest, they typically do not need to state that they are honest; honesty shows through their actions. Why, then, does Nick feel the need to make a point about this? Furthermore, since he has made this statement, one would expect his actions to reflect this honesty. Instead, Nick observes many corrupt things throughout the novel and doesn't speak up about them. He knows Daisy killed Myrtle. He knows about the various affairs that occur. He sees so much going on, yet fails to tell anyone the truth. These things could be overlooked, if only he hadn't made a statement about his honesty. That one statement causes readers to mistrust him.
Another thing that might contribute to Nick's unreliability is his drinking, particularly in chapter two. He states that this is only the second time he has been drunk in his life, so we know that he is not a big drinker. However, in this scene, he does get quite drunk. It is difficult to know whether the events he recounts in this scene are entirely accurate. He is telling them from someone who cannot be relied on because of all of the drinking that he did.