[Boromir88]

Fascinating topic lmp You wouldn't happen to have the quote available would you? Certainly after discovering Faramir had let the hobbits (and the Ring) go, I can see a motivation for Denethor to seek information on them, and thus the possibility he had seen Frodo captured.

Several possibilities though to why Sauron did not find out about the Ring, if indeed Denethor had found Frodo via the palantir. One, I think is, because when Frodo was captured, he did not have the Ring, but Sam did. Therefor, even if Denethor saw this, I'm not sure how Sauron could have been tipped off the captured hobbit has a Ring. It may also explain why the Mouth believes the captive to be spies for Gondor. If Sauron discovered Denethor's snooping, it might have led him to believe "Oh, Denethor is checking in on the spies he sent in, well I have them captured now."

Also, as the UT notes, the palantiri were only a minor part of Sauron's plan, to weaken the leadership within Minas Tirith:

It must also be considered that the Stones were only a small item in Sauron's vast designs and operations: a means of dominating and deluding two of his opponents,...~Unfinished Tales: The Palantiri

I think the stones were far more important to Denethor's use, and reasons for his vast knowledge of basically everything happening within his realm, and outside it. So, there would probably be several times Denethor used his palantir, that Sauron may not have been aware of.

And as a final point, Denethor did inherit the right to use the stone, and his will was still very strong. Stronger then any of Sauron's servants, so it was Sauron himself who the UT notes was always trying to "wrench" the stone out of Denethor's control. And Denethor was pretty resilient:

Denethor could, after he had acquired the skill, learn much of the distant events by the use of the Anor-stone alone, and even after Sauron became aware of his operations he could still do so, as long as he retained the strength to control his Stone to his own purposes;...~ibid

I am still very interested if you can track down the reference that Denethor might have known, and seen Frodo was captured. I have not even considered this before, and it's really fascinating after all these years, you can still learn new insight and perspective.