First of all, Gatsby comes right out and asks Nick what he thinks of him. This is an odd question for anyone to ask, given that socially it would be considered rude. Stranger still is that he does not give Nick time to answer, he just moves forward with telling Nick a bunch of things about himself.
The second thing that is odd, is that Gatsby says he is from the "middle-west". When Nick asks what part, he says "San Francisco" which is on the far west coast.
The third thing that is odd, even though Nick is feeling like everything Gatsby says is a lie, is when Gatsby actually pulls out a couple pieces of evidence that he is actually telling the truth! He shows Nick a medal from Montenegro and a picture of him at Oxford.