Not all that much, though he is more or less on the right track.

"Multiple girls spending a lot of time with him, false transcripts that were clearly unnecessary, a fast sexual relationship with Ms. Xiao Long... What if what he was hiding is some sort of seduction or mind control Semblance?" he mused to himself. It was the only thing that came to mind that made any kind of logical sense. If he was merely acting like he hadn't known what Aura was upon arrival, it would no doubt be, in his mind, a perfect means of deflecting any suspicion of any untoward behavior.

That explained the fake transcripts. As well as Jaune's seeming popularity with the female members of Beacon. And another thing had Ozpin rather concerned. Shortly after he had told Glynda to keep an eye on Mr. Arc, he had gotten more cautious in his movements for a while after. Which led Ozpin to the alarming suspicion that Glynda had already been compromised where Jaune was concerned.

If it was a mind control Semblance, then how exactly did it work? Semblances that controlled the mind were extremely rare, but not unheard of. And they were usually quite restrictive, in what they could make the victims do, and also requiring some sort of condition to use. Perhaps he could only control women? Possible, though they may simply have been his main target for obvious reasons.

The question then was... What to do about the young Arc? Best case scenario, he was nothing more than some horny teenager using his power to satisfy his desires. Not ideal, but not something Ozpin couldn't salvage. A stern reprimand, harsh punishment, and a closer eye on him, and perhaps he could still be steered in the right direction to use his abilities for the benefit of Remnant. After all, he had forgiven far worse in the past. And combat Semblances were not of much use in the fight he so desperately needed to find a way to win. He'd need all the mind tricks he could get his hands on.

But then there was the worst case scenario... That the young Arc was one of Salem's agents. In that case... He would need to be dealt with as an enemy.