The familiar expression that Nick Carraway notices that Gatsby frequently uses is "old sport". Gatsby uses the phrase to address male characters. In order to understand its meaning it should be taken into account that it is a term of endearment used in the twentieth century. It expresses the affection that Gatsby felt towards Nick.
It could be said that the use of this term shows Gatsby true self. He wants to be taken as a man who comes from old money backgrounds, he does not want the world to see him as a new rich. Perhaps, by using this language he can hide his real personality as well.