What scandalous information does Nick discover about Jordan later that summer?

Nick Carroway, when he meets up with Jordan Baker later in the summer, finally realizes she is "incurably dishonest" (Fitzgerald 63).  While he is enjoying his time with her, his ego flattered by her presence because "she is a golf champion and everyone knows her name" (62), he begins to see her essential dishonesty.  He takes note of her leaving someone else's car out with its top down in the rain and not admitting she is at fault.  Then he remembers why she had seemed somewhat familiar to him in the first place.  There had been a scandal about her playing golf in a big tournament.  The rumor was that she moved the ball, which is forbidden of course. It was covered up afterward, at least not reported in the news, but the rumors had reached Nick somehow.

This revelation about Jordan's dishonesty is followed by his dismissing it at as unimportant "in a woman" (63), so he is interested in pursuing his relationship with her.  This suggests that he does think honesty is important in a man, but our disingenuous narrator shares that he is still writing to that girl back west, the one whom he denies being engaged to.  He says he feels he must extricate himself from that relationship first. Then he calls himself "one of the few honest people I have ever known" (64). To carry on with Jordan and to write to the girl back home is hardly honest, and Nick in his own way is as dishonest as Jordan.