Oh, I just LOVE discussing rumors about Gatsby. That chapter that focuses on Gatsby's party ends up being a nice melting pot of rumor and Roaring Twenties recklessness, doesn't it? Gotta love that!
Here's the set of rumors that makes me chuckle the most:
The two girls and Jordan leaned together confidentially.
"Somebody told me they thought he killed a man once."
A thrill passed over all of us. The three Mr. Mumbles bent forward and listened eagerly.
"I don't think it's so much that," argued Lucille sceptically; "it's more that he was a German spy during the war."
One of the men nodded in confirmation.
Hahaha! The first of these two rumors set together makes me laugh the hardest. Note the actual wording here, ... Jordan (a girl of questionable morals anyway) says that "somebody" said that they "thought" Gatsby killed a man "once." This is total hearsay! Jordan doesn't even know who the person was who said this. That person, whoever it was, only "thought" that the Gatsby committed a murder. And the word "once" indicates that the timing can't even be confirmed. Anybody who believes this nonsense is an idiot. The irony is, considering Gatsby's involvement in the war, it's possible and even probably that he killed some folks on the other side! Ha!
The first post does a good job of listing rumors. But let's think about why Fitzgerald includes the rumors. I think that is part of what you mean by discussing the rumors at length.
I believe that the rumors that other people spread about Gatsby are included to show how concerned the society was with status and with "bloodlines." Fitzgerald is pointing out to us that the people who come to Gatsby's parties are very interested in his background. This is important because it is Gatsby's background that dooms him; it is this background that makes him unacceptable to Daisy.
I'm not sure I can list ALL the rumors about Gatsby in the novel, but I will help you with the ones I am familiar with.
It is rumored that Gatsby was a German spy. Some said that he once killed a man, that he was a bootlegger, and that he owned a string of Drug Stores. He supposedly also had ties to organized crime, and was the nephew of German Kaiser Wilhelm.
Gatsby himself started a few "rumors" about himself to increase the intrigue surrounding him. Among those included the rumor that he was given a medal for heroism by the country of Montenegro, and that he went to college at Oxford.