A very interesting question indeed. The nose has achieved remarkable symbolic importance throughout history. It is probably the most recognisable facial feature and its absence is immediately noticeable. I am sure that F. Scott Fitzgerald did not intend for the nose to have a singular symbolic value but that reference to it has to be interpreted within the context of each mention.
Tom Buchanan breaking Myrtle's nose has a dual symbolic value - firstly, it indicates his perception of Myrtle. She is nothing more than an object to him. Her sole purpose is to fulfill his lust and to stroke his ego. Her dream of sharing a life with him is shattered in this one moment of violence, for obviously, Myrtle realizes that Tom will never leave Daisy for her. This is the second aspect of the nose, in this instance, as symbol - it indicates that Tom feels for Daisy and this feeling for his wife is greater than what he feels for Myrtle. His violent reaction is, after all, provoked by Myrtle derisively and repeatedly shouting out Daisy's name. Tom finds this offensive and strikes her.
The fact that the billboard featuring Dr. Eckleburg's face sans its nose is symbolic of the decay found in the Valley of Ashes. It is a grey, disheartening place where dreams come to die. Its only significance is that it provides passage from one very wealthy area to another. It is a featureless, drab, dusty area which reeks of broken dreams. Just as Dr. Eckleburg's face lacks its definitive character, so too does the Valley of Ashes lack character. It is a place that one just passes through and forgets once one has left.
Meyer Wolfshiem's nose is symbolic of the rough and tumble life experienced by those who are career criminals. Their noses are misshapen and crooked. Criminals are commonly depicted like this and one is very wary or suspicious of such characters, even in real life. Meyer Wolfshiem's nose presents him as a shady character (which he is), one that should be avoided. It is a pity then that Jay Gatsby associated with him.
References to the butler's nose could symbolize different things. Firstly, it paints a picture of the idle rich indulging in insignificant gossip. They are bored and need something to do, so they gossip. It is also an indication of Daisy's unwillingness to seriously discuss the problems in her marriage to Tom. She avoids the issue by bringing up this irrelevant topic. Furthermore, the fact that the butler has developed a "blue nose" by polishing huge quantities of silver may symbolize the sacrifices many made to achieve the American Dream. Unfortunately, most gave up and the closest they came was to touch and see the material wealth of others, the promise of achieving the dream, just as the butler did.
Finally, one should also realize that the nose has always been perceived as that feature which provides character to a face. Many of our expressions are derived from references to the nose, since its prominent position on our faces makes it unmistakable and profoundly noticeable.