Possibly the first concrete hints are the phone calls from exotic locations that Gatsby received during the first party at his mansion. He is called away from his guests to take a call from Chicago, and later from Philadelphia. The nature of the calls is never explained by Gatsby, which helps his guests advance their whispered rumors that he had killed someone.
Rumors that he was a bootlegger come to Nick one Sunday morning. The exact nature of Gatsby's relationship with Mr. Wolfsheim is unclear, but he seems to be involved with Gatsby and large amounts of money, as evidenced when Nick overhears Wolfsheim tell Gatsby about a recent transaction.
I handed the money to Katspaugh and I said: 'All right, Katspaugh, don't pay him a penny till he shuts his mouth.' He shut it then and there.
When Wolfsheim asks if Nick is "looking for a business gonnegtion," Gatsby quickly explains that Nick is "just a friend." After Wolfsheim leaves, Gatsby informs Nick that Wolfsheim is a gambler. Gatsby's association with "the man who fixed the World's Series back in 1919" would have raised more questions in Nick's mind about how Gatsby got his money.